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System Matrices (system + matrix)
Selected AbstractsA unified approach for the formulation of interaction problems by the boundary element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2006Yalcín Mengi Abstract A unified formulation is presented, based on boundary element method, in a form suitable for performing the interaction analyses by substructure method for solid,solid and soil,structure problems. The proposed formulation permits the evaluation of all the elements of impedance and input motion matrices simultaneously at a single step in terms of system matrices of the boundary element method without solving any special problem, such as, unit displacement or load problem, as required in conventional methods. It eliminates further the complicated procedure and the need for using scattering analysis in the evaluation of input motion functions. To explain the formulation, it is first given for an inclusion interacting with an infinite surrounding medium under the influence of a seismic input, where both the inclusion and surrounding medium are treated as viscoelastic. It is shown that the formulation for a rigid inclusion may be obtained from that for flexible inclusion as a special case through a transformation. Then, the formulation is extended to other types of interaction problems: a multi-inclusion problem and an interaction problem involving a foundation embedded in a viscoelastic half-space. It is found that the proposed formulation remains essentially the same for all kinds of interaction problems and it can be used not only in regular interaction analysis, but also in the analysis involving diffraction of waves in a medium containing holes. Copyright © 2005 John Wiley & Sons, Ltd. [source] Meshless Galerkin analysis of Stokes slip flow with boundary integral equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2009Xiaolin Li Abstract This paper presents a novel meshless Galerkin scheme for modeling incompressible slip Stokes flows in 2D. The boundary value problem is reformulated as boundary integral equations of the first kind which is then converted into an equivalent variational problem with constraint. We introduce a Lagrangian multiplier to incorporate the constraint and apply the moving least-squares approximations to generate trial and test functions. In this boundary-type meshless method, boundary conditions can be implemented exactly and system matrices are symmetric. Unlike the domain-type method, this Galerkin scheme requires only a nodal structure on the bounding surface of a body for approximation of boundary unknowns. The convergence and abstract error estimates of this new approach are given. Numerical examples are also presented to show the efficiency of the method. Copyright © 2009 John Wiley & Sons, Ltd. [source] Robust H, filtering for switched linear discrete-time systems with polytopic uncertaintiesINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 6 2006Lixian Zhang Abstract In this paper, the problem of robust H, filtering for switched linear discrete-time systems with polytopic uncertainties is investigated. Based on the mode-switching idea and parameter-dependent stability result, a robust switched linear filter is designed such that the corresponding filtering error system achieves robust asymptotic stability and guarantees a prescribed H, performance index for all admissible uncertainties. The existence condition of such filter is derived and formulated in terms of a set of linear matrix inequalities (LMIs) by the introduction of slack variables to eliminate the cross coupling of system matrices and Lyapunov matrices among different subsystems. The desired filter can be constructed by solving the corresponding convex optimization problem, which also provides an optimal H, noise-attenuation level bound for the resultant filtering error system. A numerical example is given to show the effectiveness and the potential of the proposed techniques. Copyright © 2006 John Wiley & Sons, Ltd. [source] Closed-loop identification of the time-varying dynamics of variable-speed wind turbinesINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 1 2009J. W. van Wingerden Abstract The trend with offshore wind turbines is to increase the rotor diameter as much as possible to decrease the costs per kWh. The increasing dimensions have led to the relative increase in the loads on the wind turbine structure. Because of the increasing rotor size and the spatial load variations along the blade, it is necessary to react to turbulence in a more detailed way: each blade separately and at several separate radial distances. This combined with the strong nonlinear behavior of wind turbines motivates the need for accurate linear parameter-varying (LPV) models for which advanced control synthesis techniques exist within the robust control framework. In this paper we present a closed-loop LPV identification algorithm that uses dedicated scheduling sequences to identify the rotational dynamics of a wind turbine. We assume that the system undergoes the same time variation several times, which makes it possible to use time-invariant identification methods as the input and the output data are chosen from the same point in the variation of the system. We use time-invariant techniques to identify a number of extended observability matrices and state sequences that are inherent to subspace identification identified in a different state basis. We show that by formulating an intersection problem all states can be reconstructed in a general state basis from which the system matrices can be estimated. The novel algorithm is applied on a wind turbine model operating in closed loop. Copyright © 2008 John Wiley & Sons, Ltd. [source] Augmented Lyapunov functional and delay-dependent stability criteria for neutral systemsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 18 2005Yong He Abstract In this paper, an augmented Lyapunov functional is proposed to investigate the asymptotic stability of neutral systems. Two methods with or without decoupling the Lyapunov matrices and system matrices are developed and shown to be equivalent to each other. The resulting delay-dependent stability criteria are less conservative than the existing ones owing to the augmented Lyapunov functional and the introduction of free-weighting matrices. The delay-independent criteria are obtained as an easy corollary. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods. Copyright © 2005 John Wiley & Sons, Ltd. [source] Robust Kalman filtering for uncertain discrete-time linear systemsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 13 2003Germain Garcia Abstract This paper presents a steady-state robust state estimator for a class of uncertain discrete-time linear systems with norm-bounded uncertainty. It is shown that if the system satisfies some particular structural conditions and if the uncertainty has a specific structure, the gain of the robust estimator (which assures a guaranteed cost) can be calculated using a formula only involving the original system matrices. Among the conditions the system has to satisfy, the strongest one relies on a minimum phase argument. It is also shown that under the assumptions considered, the robust estimator is in fact the Kalman filter for the nominal system. Copyright © 2003 John Wiley & Sons, Ltd. [source] An alternative analytical reduction scheme in the time-domain layered finite element reduction recovery method for high-frequency IC designMICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 9 2008Houle Gan Abstract An alternative analytical reduction scheme was proposed in the time-domain layered finite element reduction recovery (LAFE-RR) method for the analysis of high-frequency integrated circuits. This alternative reduction scheme permits the use of general absorbing boundary conditions in the framework of a time-domain LAFE-RR method. In addition, it allows for an application of the LAFE-RR method to circuit problems in which the system matrices in multiple regions need to be reduced separately. Numerical and experimental results are given to demonstrate its validity. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 2337,2341, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23630 [source] A preconditioner for generalized saddle point problems: Application to 3D stationary Navier-Stokes equationsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2006C. Calgaro Abstract In this article we consider the stationary Navier-Stokes system discretized by finite element methods which do not satisfy the inf-sup condition. These discretizations typically take the form of a variational problem with stabilization terms. Such a problem may be transformed by iteration methods into a sequence of linear, Oseen-type variational problems. On the algebraic level, these problems belong to a certain class of linear systems with nonsymmetric system matrices ("generalized saddle point problems"). We show that if the underlying finite element spaces satisfy a generalized inf-sup condition, these problems have a unique solution. Moreover, we introduce a block triangular preconditioner and we show how the eigenvalue bounds of the preconditioned system matrix depend on the coercivity constant and continuity bounds of the bilinear forms arising in the variational problem. Finally we prove that the stabilized P1-P1 finite element method proposed by Rebollo is covered by our theory and we show that the condition number of the preconditioned system matrix is independent of the mesh size. Numerical tests with 3D stationary Navier-Stokes flows confirm our results. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2006 [source] Delay-dependent robust passive control for a class of nonlinear systems with time-varying delaysOPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 5 2008Jiqing Qiu Abstract In this paper, the problem of robust passive control for a class of nonlinear systems with time-varying delays is considered. The uncertainties investigated in this paper are norm bounded and time varying, and they enter all system matrices. Based on the Lyapunov,Krasovskii functionals approach, a new robust passive control criterion is proposed in terms of linear matrix inequalities, which is dependent on the size of time delay. We also design a state feedback controller that guarantees a robust asymptotically stable and strictly passive closed-loop system for all admissible uncertainties. Finally, two numerical examples are given to illustrate the effectiveness of the developed techniques. Copyright © 2007 John Wiley & Sons, Ltd. [source] Stability of Linear Parameter Varying and Linear Switching SystemsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003Fabian Wirth We consider stability of families of linear time-varying systems, that are determined by a set of time-varying parameters which adhere to certain rules. The conditions are general enough to encompass on the one hand stability questions for systems that are frequently called linear parameter varying systems in the literature and on the other hand also linear switching systems, in which parameter variations are allowed to have discontinuities. Combinations of these two sets of assumptions are also possible within the framework studied here. Under the assumption of irreducibility of the sets of system matrices, we show how to construct parameter dependent Lyapunov functions for the systems under consideration that exactly characterize the exponential growth rate. It is clear that such Lyapunov functions do not exist in general. But every system of our class can be reduced to a finite number of subsystems for which irreducibility holds. [source] Impulsive-mode controllablizability revisited for descriptor linear systems,ASIAN JOURNAL OF CONTROL, Issue 3 2009Ai-Guo Wu Abstract New criteria for impulsive-mode controllablizability of descriptor linear systems are proposed by adopting the null space approach. The range of the possible dynamical orders of the closed-loop system with impulsive-mode controllability is characterized in terms of the original system matrices. Moreover, the parametric expressions of the impulsive-mode controllablizing controllers are also established. Since only the orthogonal transformations are involved, the design approach is numerically stable. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source] On stability and stabilizability of positive delay systems,ASIAN JOURNAL OF CONTROL, Issue 2 2009Ligang Wu Abstract The stabilization problem with positivity is investigated in this note for discrete-time linear systems with time delay. A delay-independent necessary and sufficient condition is proposed in terms of linear matrix inequalities (LMIs) for the existence of desired controllers that guarantee the closed-loop system to be asymptotically stable and positive. In addition, the obtained result is further extended to more general case when the system matrices contain uncertain parameters, where a sufficient condition is obtained. The frequently used polytopic parameter uncertainty is taken into consideration. Since the conditions obtained are expressed as LMIs, which can be easily verified by using standard numerical software. A numerical example is provided to illustrate the proposed results. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source] LMI APPROACH TO ROBUST FILTERING FOR DISCRETE TIME-DELAY SYSTEMS WITH NONLINEAR DISTURBANCESASIAN JOURNAL OF CONTROL, Issue 2 2005Huijun Gao ABSTRACT This paper investigates the problem of robust filtering for a class of uncertain nonlinear discrete-time systems with multiple state delays. It is assumed that the parameter uncertainties appearing in all the system matrices reside in a polytope, and that the nonlinearities entering into both the state and measurement equations satisfy global Lipschitz conditions. Attention is focused on the design of robust full-order and reduced-order filters guaranteeing a prescribed noise attenuation level in an H, or l2 - l, sense with respect to all energy-bounded noise disturbances for all admissible uncertainties and time delays. Both delay-dependent and independent approaches are developed by using linear matrix inequality (LMI) techniques, which are applicable to systems either with or without a priori information on the size of delays. [source] A relation between the logarithmic capacity and the condition number of the BEM-matricesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2007W. Dijkstra Abstract We establish a relation between the logarithmic capacity of a two-dimensional domain and the solvability of the boundary integral equation for the Laplace problem on that domain. It is proved that when the logarithmic capacity is equal to one the boundary integral equation does not have a unique solution. A similar result is derived for the linear algebraic systems that appear in the boundary element method. As these systems are based on the boundary integral equation, no unique solution exists when the logarithmic capacity is equal to one. Hence, the system matrix is ill-conditioned. We give several examples to illustrate this and investigate the analogies between the Laplace problem with Dirichlet and mixed boundary conditions. Copyright © 2006 John Wiley & Sons, Ltd. [source] P-wave and S-wave decomposition in boundary integral equation for plane elastodynamic problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2003Emmanuel Perrey-Debain Abstract The method of plane wave basis functions, a subset of the method of Partition of Unity, has previously been applied successfully to finite element and boundary element models for the Helmholtz equation. In this paper we describe the extension of the method to problems of scattering of elastic waves. This problem is more complicated for two reasons. First, the governing equation is now a vector equation and second multiple wave speeds are present, for any given frequency. The formulation has therefore a number of novel features. A full development of the necessary theory is given. Results are presented for some classical problems in the scattering of elastic waves. They demonstrate the same features as those previously obtained for the Helmholtz equation, namely that for a given level of error far fewer degrees of freedom are required in the system matrix. The use of the plane wave basis promises to yield a considerable increase in efficiency over conventional boundary element formulations in elastodynamics. Copyright © 2003 John Wiley & Sons, Ltd. [source] Radial point interpolation based finite difference method for mechanics problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2006G. R. Liu Abstract A radial point interpolation based finite difference method (RFDM) is proposed in this paper. In this novel method, radial point interpolation using local irregular nodes is used together with the conventional finite difference procedure to achieve both the adaptivity to irregular domain and the stability in the solution that is often encountered in the collocation methods. A least-square technique is adopted, which leads to a system matrix with good properties such as symmetry and positive definiteness. Several numerical examples are presented to demonstrate the accuracy and stability of the RFDM for problems with complex shapes and regular and extremely irregular nodes. The results are examined in detail in comparison with other numerical approaches such as the radial point collocation method that uses local nodes, conventional finite difference and finite element methods. Copyright © 2006 John Wiley & Sons, Ltd. [source] Convergence properties of bias-eliminating algorithms for errors-in-variables identificationINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 9 2005Torsten Söderström Abstract This paper considers the problem of dynamic errors-in-variables identification. Convergence properties of the previously proposed bias-eliminating algorithms are investigated. An error dynamic equation for the bias-eliminating parameter estimates is derived. It is shown that the convergence of the bias-eliminating algorithms is basically determined by the eigenvalue of largest magnitude of a system matrix in the estimation error dynamic equation. When this system matrix has all its eigenvalues well inside the unit circle, the bias-eliminating algorithms can converge fast. In order to avoid possible divergence of the iteration-type bias-eliminating algorithms in the case of high noise, the bias-eliminating problem is re-formulated as a minimization problem associated with a concentrated loss function. A variable projection algorithm is proposed to efficiently solve the resulting minimization problem. A numerical simulation study is conducted to demonstrate the theoretical analysis. Copyright © 2005 John Wiley & Sons, Ltd. [source] A comparison of small gain versus Lyapunov type robust stability boundsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 15 2001Jie Chen Abstract We address stability issues pertaining to perturbed linear time-invariant systems described by state space models. We show that for a class of highly structured uncertainties in the system matrix, a robust stability bound given by the complex structured singular value is less conservative than that obtained via Lyapunov approach. This result thus provides a counterpart to an earlier one pertaining to unstructured uncertainties, and serves to extend and support the statement that frequency domain small gain conditions may often be less conservative than those time domain criteria obtained using Lyapunov approach. Copyright © 2001 John Wiley & Sons, Ltd. [source] Implicit nonstaggered finite-difference time-domain methodMICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 4 2005Shumin Wang Abstract A new, unconditionally stable, implicit nonstaggered finite-difference time-domain (INS-FDTD) method is introduced. This method is more efficient than the (unconditionally stable) finite-element time-domain (FETD) method with brick elements because the number of nonzero elements in the system matrix is reduced. A numerical-dispersion analysis is provided as well. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 45: 317,319, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20809 [source] A comparison of abstract versions of deflation, balancing and additive coarse grid correction preconditionersNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 4 2008R. Nabben Abstract In this paper we consider various preconditioners for the conjugate gradient (CG) method to solve large linear systems of equations with symmetric positive definite system matrix. We continue the comparison between abstract versions of the deflation, balancing and additive coarse grid correction preconditioning techniques started in (SIAM J. Numer. Anal. 2004; 42:1631,1647; SIAM J. Sci. Comput. 2006; 27:1742,1759). There the deflation method is compared with the abstract additive coarse grid correction preconditioner and the abstract balancing preconditioner. Here, we close the triangle between these three methods. First of all, we show that a theoretical comparison of the condition numbers of the abstract additive coarse grid correction and the condition number of the system preconditioned by the abstract balancing preconditioner is not possible. We present a counter example, for which the condition number of the abstract additive coarse grid correction preconditioned system is below the condition number of the system preconditioned with the abstract balancing preconditioner. However, if the CG method is preconditioned by the abstract balancing preconditioner and is started with a special starting vector, the asymptotic convergence behavior of the CG method can be described by the so-called effective condition number with respect to the starting vector. We prove that this effective condition number of the system preconditioned by the abstract balancing preconditioner is less than or equal to the condition number of the system preconditioned by the abstract additive coarse grid correction method. We also provide a short proof of the relationship between the effective condition number and the convergence of CG. Moreover, we compare the A -norm of the errors of the iterates given by the different preconditioners and establish the orthogonal invariants of all three types of preconditioners. Copyright © 2008 John Wiley & Sons, Ltd. [source] Robust parameter-free algebraic multilevel preconditioningNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 6-7 2002Y. Notay Abstract To precondition large sparse linear systems resulting from the discretization of second-order elliptic partial differential equations, many recent works focus on the so-called algebraic multilevel methods. These are based on a block incomplete factorization process applied to the system matrix partitioned in hierarchical form. They have been shown to be both robust and efficient in several circumstances, leading to iterative solution schemes of optimal order of computational complexity. Now, despite the procedure is essentially algebraic, previous works focus generally on a specific context and consider schemes that use classical grid hierarchies with characteristic mesh sizes h,2h,4h, etc. Therefore, these methods require some extra information besides the matrix of the linear system and lack of robustness in some situations where semi-coarsening would be desirable. In this paper, we develop a general method that can be applied in a black box fashion to a wide class of problems, ranging from 2D model Poisson problems to 3D singularly perturbed convection,diffusion equations. It is based on an automatic coarsening process similar to the one used in the AMG method, and on coarse grid matrices computed according to a simple and cheap aggregation principle. Numerical experiments illustrate the efficiency and the robustness of the proposed approach. Copyright © 2002 John Wiley & Sons, Ltd. [source] A preconditioner for generalized saddle point problems: Application to 3D stationary Navier-Stokes equationsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2006C. Calgaro Abstract In this article we consider the stationary Navier-Stokes system discretized by finite element methods which do not satisfy the inf-sup condition. These discretizations typically take the form of a variational problem with stabilization terms. Such a problem may be transformed by iteration methods into a sequence of linear, Oseen-type variational problems. On the algebraic level, these problems belong to a certain class of linear systems with nonsymmetric system matrices ("generalized saddle point problems"). We show that if the underlying finite element spaces satisfy a generalized inf-sup condition, these problems have a unique solution. Moreover, we introduce a block triangular preconditioner and we show how the eigenvalue bounds of the preconditioned system matrix depend on the coercivity constant and continuity bounds of the bilinear forms arising in the variational problem. Finally we prove that the stabilized P1-P1 finite element method proposed by Rebollo is covered by our theory and we show that the condition number of the preconditioned system matrix is independent of the mesh size. Numerical tests with 3D stationary Navier-Stokes flows confirm our results. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2006 [source] Determination of pseudophakic accommodation with translation lenses using Purkinje image analysisOPHTHALMIC AND PHYSIOLOGICAL OPTICS, Issue 2 2005Achim Langenbucher Abstract Purpose:, To determine pseudophakic accommodation of an accommodating posterior chamber intraocular lens (translation lens) using Purkinje image analysis and linear matrix methods in the paraxial space. Methods:, A 2 × 2 system matrix was defined for each Purkinje image I to IV using refraction, translation and mirror matrices. Image size (m) and axial image position (z) was determined as an example for an off-axis object (a 0.2 m off-axis object located 0.5 m in front of the cornea.). First, our method was applied to the phakic relaxed (emmetropic) and accommodated (6.96 D) Le Grand eye. Secondly, for demonstration of the applicability of the calculation scheme to the pseudophakic eye, we provide a clinical example where we determine the accommodation amplitude of the translation lens (1 CU, HumanOptics, Erlangen, Germany) from photographed Purkinje images in the relaxed and accommodated state. From the biometric data: axial length 23.7 mm, corneal power 43.5, corneal thickness 550 microns, implanted intraocular lens (IOL) with a refractive power of 20.5 D (shape equi-biconvex, refractive index 1.46), and refractive indices of the cornea, aqueous and vitreous from the Le Grand model eye, we calculated the refractive state and the sizes of Purkinje images I and III initiated from two off-axis light sources. Results:, For the Le Grand model eye, Purkinje image II (z/m = 3.5850 mm/0.0064) is slightly smaller than and directly in front of image I (z/m = 3.8698 mm/0.0077). Purkinje image III (z/m = 10.6097 mm/0.0151) is nearly double the size of image I and during accommodation it moves from the vitreous into the crystalline lens. Purkinje IV (z/m = 4.3244 mm/,0.0059) is inverted, three quarters the size of image I, lies in the crystalline lens and moves slightly towards the retina. For the pseudophakic eye, pseudophakic accommodation of 1.10 D was calculated from the proportion of distances between both Purkinje images I and III in the relaxed (3.04) and accommodated (2.75) state, which is in contrast to the total subjective accommodation of 2.875 D evaluated with an accommodometer. Conclusions:, We present a straightforward mathematical strategy for calculation of the Purkinje images I,IV. Results of our model calculation resemble the values provided by Le Grand. In addition, this approach yields a simple en bloc scheme for determination of pseudophakic accommodation in pseudophakic eyes with accommodative lenses (translation lenses) using Purkinje image photography. [source] Robust hyperplane synthesis for sliding mode control systems via sensitivity minimizationOPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 3 2002Hei Ka Tam Abstract A robust hyperplane computation scheme for sliding mode control systems is proposed in this paper. A novel sensitivity index for the sliding eigenvalues with respect to perturbations in the system matrix, the input matrix and the hyperplane matrix is derived in the first instance. The robust hyperplane design problem is then formulated as an optimization task in which the proposed sensitivity index is accordingly minimized. Gradient information of the objective function is established which permits optimization to be proceeded effectively. A numerical example with statistical testing is employed to illustrate the design technique. Copyright © 2002 John Wiley & Sons, Ltd. [source] Wavelets in state space modelsAPPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 3 2003Eliana Zandonade Abstract In this paper, we consider the utilization of wavelets in conjunction with state space models. Specifically, the parameters in the system matrix are expanded in wavelet series and estimated via the Kalman Filter and the EM algorithm. In particular this approach is used for switching models. Two applications are given, one to the problem of detecting the paths of targets using an array of sensors, and the other to a series of daily spreads between two Brazilian bonds. Copyright © 2003 John Wiley & Sons, Ltd. [source] Computational relaxed TP model transformation: restricting the computation to subspaces of the dynamic model,ASIAN JOURNAL OF CONTROL, Issue 5 2009Szabolcs Nagy Abstract The tensor-product (TP) model transformation is a recently proposed numerical method capable of transforming linear parameter varying state-space models to the higher order singular value decomposition (HOSVD) based canonical form of polytopic models. It is also capable of generating various types of convex TP models, a type of polytop models, for linear matrix inequality based controller design. The crucial point of the TP model transformation is that its computational load exponentially explodes with the dimensionality of the parameter vector of the parameter-varying state-space model. In this paper we propose a modified TP model transformation that leads to considerable reduction of the computation. The key idea of the method is that instead of transforming the whole system matrix at once in the whole parameter space, we decompose the problem and perform the transformation element wise and restrict the computation to the subspace where the given element of the model varies. The modified TP model transformation can readily be executed in higher dimensional cases when the original TP model transformation fails. The effectiveness of the new method is illustrated with numerical examples. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source] | |||||||||||||||||||||||||