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Original System (original + system)
Selected AbstractsStability of linear time-periodic delay-differential equations via Chebyshev polynomialsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2004Eric A. Butcher Abstract This paper presents a new technique for studying the stability properties of dynamic systems modeled by delay-differential equations (DDEs) with time-periodic parameters. By employing a shifted Chebyshev polynomial approximation in each time interval with length equal to the delay and parametric excitation period, the dynamic system can be reduced to a set of linear difference equations for the Chebyshev expansion coefficients of the state vector in the previous and current intervals. This defines a linear map which is the ,infinite-dimensional Floquet transition matrix U'. Two different formulas for the computation of the approximate U, whose size is determined by the number of polynomials employed, are given. The first one uses the direct integral form of the original system in state space form while the second uses a convolution integral (variation of parameters) formulation. Additionally, a variation on the former method for direct application to second-order systems is also shown. An error analysis is presented which allows the number of polynomials employed in the approximation to be selected in advance for a desired tolerance. An extension of the method to the case where the delay and parametric periods are commensurate is also shown. Stability charts are produced for several examples of time-periodic DDEs, including the delayed Mathieu equation and a model for regenerative chatter in impedance-modulated turning. The results indicate that this method is an effective way to study the stability of time-periodic DDEs. Copyright © 2004 John Wiley & Sons, Ltd. [source] A collocated, iterative fractional-step method for incompressible large eddy simulationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2008Giridhar Jothiprasad Abstract Fractional-step methods are commonly used for the time-accurate solution of incompressible Navier,Stokes (NS) equations. In this paper, a popular fractional-step method that uses pressure corrections in the projection step and its iterative variants are investigated using block-matrix analysis and an improved algorithm with reduced computational cost is developed. Since the governing equations for large eddy simulation (LES) using linear eddy-viscosity-based sub-grid models are similar in form to the incompressible NS equations, the improved algorithm is implemented in a parallel LES solver. A collocated grid layout is preferred for ease of extension to curvilinear grids. The analyzed fractional-step methods are viewed as an iterative approximation to a temporally second-order discretization. At each iteration, a linear system that has an easier block-LU decomposition compared with the original system is inverted. In order to improve the numerical efficiency and parallel performance, modified ADI sub-iterations are used in the velocity step of each iteration. Block-matrix analysis is first used to determine the number of iterations required to reduce the iterative error to the discretization error of. Next, the computational cost is reduced through the use of a reduced stencil for the pressure Poisson equation (PPE). Energy-conserving, spatially fourth-order discretizations result in a 7-point stencil in each direction for the PPE. A smaller 5-point stencil is achieved by using a second-order spatial discretization for the pressure gradient operator correcting the volume fluxes. This is shown not to reduce the spatial accuracy of the scheme, and a fourth-order continuity equation is still satisfied to machine precision. The above results are verified in three flow problems including LES of a temporal mixing layer. Copyright © 2008 John Wiley & Sons, Ltd. [source] Approaches to knowledge reductions in inconsistent systemsINTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 9 2003Wen-Xiu Zhang This article deals with approaches to knowledge reductions in inconsistent information systems (ISs). The main objective of this work was to introduce a new kind of knowledge reduction called a maximum distribution reduct, which preserves all maximum decision classes. This type of reduction eliminates the harsh requirements of the distribution reduct and overcomes the drawback of the possible reduct that the derived decision rules may be incompatible with the ones derived from the original system. Then, the relationships among the maximum distribution reduct, the distribution reduct, and the possible reduct were discussed. The judgement theorems and discernibility matrices associated with the three reductions were examined, from which we can obtain approaches to knowledge reductions in rough set theory (RST). © 2003 Wiley Periodicals, Inc. [source] Positivity and time behavior of a linear reaction,diffusion system, non-local in space and timeMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 15 2008Andrii Khrabustovskyi Abstract We consider a general linear reaction,diffusion system in three dimensions and time, containing diffusion (local interaction), jumps (nonlocal interaction) and memory effects. We prove a maximum principle and positivity of the solution and investigate its asymptotic behavior. Moreover, we give an explicit expression of the limit of the solution for large times. In order to obtain these results, we use the following method: We construct a Riemannian manifold with complicated microstructure depending on a small parameter. We study the asymptotic behavior of the solution to a simple diffusion equation on this manifold as the small parameter tends to zero. It turns out that the homogenized system coincides with the original reaction,diffusion system. Using this and the facts that the diffusion equation on manifolds satisfies the maximum principle and its solution converges to a easily calculated constant, we can obtain analogous properties for the original system. Copyright © 2008 John Wiley & Sons, Ltd. [source] Asymptotic and spectral properties of operator-valued functions generated by aircraft wing modelMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 3 2004A. V. Balakrishnan Abstract The present paper is devoted to the asymptotic and spectral analysis of an aircraft wing model in a subsonic air flow. The model is governed by a system of two coupled integro-differential equations and a two parameter family of boundary conditions modelling the action of the self-straining actuators. The differential parts of the above equations form a coupled linear hyperbolic system; the integral parts are of the convolution type. The system of equations of motion is equivalent to a single operator evolution,convolution equation in the energy space. The Laplace transform of the solution of this equation can be represented in terms of the so-called generalized resolvent operator, which is an operator-valued function of the spectral parameter. More precisely, the generalized resolvent is a finite-meromorphic function on the complex plane having a branch-cut along the negative real semi-axis. Its poles are precisely the aeroelastic modes and the residues at these poles are the projectors on the generalized eigenspaces. The dynamics generator of the differential part of the system has been systematically studied in a series of works by the second author. This generator is a non-selfadjoint operator in the energy space with a purely discrete spectrum. In the aforementioned series of papers, it has been shown that the set of aeroelastic modes is asymptotically close to the spectrum of the dynamics generator, that this spectrum consists of two branches, and a precise spectral asymptotics with respect to the eigenvalue number has been derived. The asymptotical approximations for the mode shapes have also been obtained. It has also been proven that the set of the generalized eigenvectors of the dynamics generator forms a Riesz basis in the energy space. In the present paper, we consider the entire integro-differential system which governs the model. Namely, we investigate the properties of the integral convolution-type part of the original system. We show, in particular, that the set of poles of the adjoint generalized resolvent is asymptotically close to the discrete spectrum of the operator that is adjoint to the dynamics generator corresponding to the differential part. The results of this paper will be important for the reconstruction of the solution of the original initial boundary-value problem from its Laplace transform and for the analysis of the flutter phenomenon in the forthcoming work. Copyright © 2004 John Wiley & Sons, Ltd. [source] ,, model reduction for uncertain two-dimensional discrete systemsOPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 4 2005Huijun Gao Abstract This paper investigates the problem of ,, model reduction for two-dimensional (2-D) discrete systems with parameter uncertainties residing in a polytope. For a given robustly stable system, our attention is focused on the construction of a reduced-order model, which also resides in a polytope and approximates the original system well in an ,, norm sense. Both Fornasini,Marchesini local state-space (FMLSS) and Roesser models are considered through parameter-dependent approaches, with sufficient conditions obtained for the existence of admissible reduced-order solutions. Since these obtained conditions are not expressed as strict linear matrix inequalities (LMIs), the cone complementary linearization method is exploited to cast them into sequential minimization problems subject to LMI constraints, which can be readily solved using standard numerical software. In addition, the development of zeroth order models is also presented. Two numerical examples are provided to show the effectiveness of the proposed theories. Copyright © 2005 John Wiley & Sons, Ltd. [source] Preparation of oily core polyamide microcapsules via interfacial polycondensation,POLYMER INTERNATIONAL, Issue 4 2003L Soto-Portas Abstract Microcapsules obtained by interfacial polycondensation from an original system based on the polyaddition of specific di- or polyamines and more classical acyl chloride molecules were studied. The originality of the system lies in the fact that the encapsulated agent is the internal phase allowing its incorporation without an organic solvent, which is an advantage from the point of view of environmental protection. Once the optimal parameters of the emulsion were determined, the membrane formation was studied by optimizing the emulsification and reaction times in relation to simultaneous acyl chloride hydrolysis. The microcapsules were obtained by interfacial polycondensation between an excess of amine functions (diamine and diethylenetriamine) and acyl chloride (sebacoyl chloride and 1,3,5-benzene tricarbonyl trichloride) from an oil-in-water emulsion in the presence of 88% hydrolyzed poly(vinyl alcohol) as a surfactant. Various formulations in terms of COCl concentration, crosslinking agent concentration, excess of amine functions, emulsification and reaction times were prepared. The hydrolysis of acyl halide functions is the main parameter which influences the growth of the membrane. The increase in acyl chloride function concentration allows compensation for that lost by hydrolysis, and increases the encapsulation yield to about 90%. The degree of crosslinking of the membrane was controlled in order to minimize the subsequent release of oil by the addition of trifunctional monomers. An optimal formulation was developed offering high encapsulation yield and optimal elastic behaviour. Almost spherical capsules, with a membrane thickness of approximately 500,nm, relatively smooth internal walls and crumpled external walls, were observed by scanning electron microscopy. © 2003 Society of Chemical Industry [source] Observer-based non-fragile control against measurement disturbances and controller perturbations for discrete systems with state delay ,ASIAN JOURNAL OF CONTROL, Issue 3 2009Xiaosheng Fang Abstract This paper investigates the observer-based non-fragile control problem for a class of discrete time delay systems with measurement disturbances and controller perturbations. A simultaneous state and disturbance estimation technique is developed by designing a state observer for a descriptor system obtained from the original system. Based on this observer, the design method of a non-fragile controller is then formulated and the controller design problem is transformed to a convex optimization problem, which can be solved by a linear matrix inequality approach. In this design, the additive and multiplicative forms of uncertainties which perturb the gains of control and observer are both considered. The resultant non-fragile observer-based controller guarantees that the closed-loop system is asymptotically stable and can tolerate measurement disturbances and a certain degree of controller parameter perturbation. A numerical example is given to illustrate the effectiveness of the proposed design method. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source] Robust decentralized H, control for interconnected descriptor systems with norm-bounded uncertainties,,ASIAN JOURNAL OF CONTROL, Issue 1 2009Ning Chen Abstract This paper considers a robust decentralized H, control problem for interconnected descriptor systems. The uncertainties are assumed to be time-invariant, norm-bounded, and existing in both the system and control input matrices. Our interest is focused on dynamic output feedback. A sufficient condition for an uncertain interconnected descriptor system to be robustly stabilizable H, control with a specified disturbance attenuation level is derived in terms of a nonlinear matrix inequality (NMI). A two-stage homotopy method is employed to solve the NMI iteratively. First, a decentralized controller for the nominal descriptor system is computed by imposing block-diagonal constraints on the coefficient matrices of the controller gradually. Then, the decentralized controller is gradually modified from the nominal descriptor system (without uncertainties) to the original system with uncertainties. On each stage, groups of variables are fixed alternately at the iterations to reduce the NMI to linear matrix inequalities (LMIs). An example is given to show the usefulness of this method. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source] | ||||||||||