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Robust Stability (robust + stability)

Distribution by Scientific Domains

Engineering	92%
3 Other Domains	8%

Terms modified by Robust Stability

robust stability margin

Selected Abstracts

ROBUST STABILITY AND STABILIZATION OF A CLASS OF SINGULAR SYSTEMS WITH MULTIPLE TIME-VARYING DELAYS

ASIAN JOURNAL OF CONTROL, Issue 1 2006
S. M. Saadni
ABSTRACT This paper deals with the problem of robust stability and robust stabilization for uncertain continuous singular systems with multiple time-varying delays. The parametric uncertainty is assumed to be norm bounded. The purpose of the robust stability problem is to give conditions such that the uncertain singular system is regular, impulse free, and stable for all admissible uncertainties. The purpose of the robust stabilization problem is to design a feedback control law such that the resulting closed-loop system is robustly stable. This problem is solved via generalized quadratic stability approach. A strict linear matrix inequality (LMI) design approach is developed. Finally, a numerical example is provided to demonstrate the application of the proposed method. [source]

IMPROVED CONDITIONS FOR DELAY-DEPENDENT ROBUST STABILITY AND STABILIZATION OF UNCERTAIN DISCRETE TIME-DELAY SYSTEMS

ASIAN JOURNAL OF CONTROL, Issue 3 2005
Shengyuan Xu
ABSTRACT This paper provides improved delay-dependent conditions for the robust stability and robust stabilization of discrete time-delay systems with norm-bounded parameter uncertainties. It is theoretically established that the proposed conditions are less conservative than those discussed in the literature. The new approach proposed in this paper in a derivation of delay-dependent conditions and involves the use of neither model transformation nor bounding techniques for some cross terms. A numerical example is provided to demonstrate the reduced conservatism of the proposed conditions. [source]

Robust stability of iterative learning control schemes

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 10 2008
Mark French
Abstract A notion of robust stability is developed for iterative learning control in the context of disturbance attenuation. The size of the unmodelled dynamics is captured via a gap distance, which in turn is related to the standard ,2 gap metric, and the resulting robustness certificate is qualitatively equivalent to that obtained in classical robust ,, theory. A bound on the robust stability margin for a specific adaptive ILC design is established. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Robust stability of neutral systems: a Lyapunov-Krasovskii constructive approach

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 16 2004
S.A. Rodrìguez
Abstract In this paper, robust stability of uncertain linear neutral systems is analysed via a Lyapunov,Krasovskii constructive approach. This paper is the first attempt to compute the Lyapunov,Krasovskii functional for a given time derivative functional w(·) for the class of linear neutral type time delay systems. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Robust stability and structured uncertainty bounded by the Euclidean norm

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 8 2001
Teodoro Álamo
Abstract In the context of robust stability, the , -problem is generalized for uncertainty bounded by means of the Euclidean norm. In some cases, a weighted Euclidean norm may be preferable to the infinite norm, for example, when the deviation from the nominal parameters exhibits a Gaussian distribution, also in the case that the parameters of the system are estimated by the ellipsoid algorithm. Several polynomial-time upper bounds for the new , -problem are proposed. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Controller design for natural and robotic systems with transmission delays

JOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 5 2002
Abhay Kataria
Robust stability and two-dimensional trajectory following problems are considered for n -link robotic systems with transmission delays. Such problems appear in telerobotics, where the controller is physically far from the robot, and in neural control of musculo-skeletal (biological) systems, where muscle actuation and neural sensing are subject to time delays. A typical second-order nonlinear dynamical model is taken with input and output time delays. In a prior work by the authors, a control strategy was developed for stable movement of the planar linkage system, using the standard Q -parameterization and solving an H, control problem to determine the free parameter. In this article, a new control scheme is proposed to eliminate the steady-state errors seen in the tracking performance of the controller derived in the earlier work. Simulation examples are shown to demonstrate the effectiveness of the proposed control methodology. © 2002 Wiley Periodicals, Inc. [source]

Output feedback variable structure control for a class of uncertain switched systems,

ASIAN JOURNAL OF CONTROL, Issue 1 2009
Jie Lian
Abstract This paper considers the output feedback variable structure control problem for a class of uncertain switched systems. A single sliding surface is constructed using only output information. Robust stability of the sliding motion restricted to the sliding surface is achieved and complete invariance to the matched and the mismatched uncertainties is guaranteed via a hysteresis switching law based on a reduced order observer. Output feedback variable structure controllers are given to guarantee that the redefined sliding surface is reached in finite time. A numerical example illustrates the effectiveness of the proposed design method. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source]

Robust iterative learning control design for batch processes with uncertain perturbations and initialization

AICHE JOURNAL, Issue 6 2006
Jia Shi
Abstract A robust iterative learning control (ILC) scheme for batch processes with uncertain perturbations and initial conditions is developed. The proposed ILC design is transformed into a robust control design of a 2-D Fornasini,Marchsini model with uncertain parameter perturbations. The concepts of robust stabilities and convergences along batch and time axes are introduced. The proposed design leads to nature integration of an output feedback control and a feedforward ILC to guarantee the robust convergence along both the time and the cycle directions. This design framework also allows easy enhancement of the feedback and/or feedforward controls of the system by extending the learning information along the time and/or the cycle directions. The proposed analysis and design are formulated as matrix inequality conditions that can be solved by an algorithm based on linear matrix inequality. Application to control injection packing pressure shows the proposed ILC scheme and its design are effective. © 2006 American Institute of Chemical Engineers AIChE J, 2006 [source]

Conservation and expression of IQ-domain-containing calpacitin gene products (neuromodulin/GAP-43, neurogranin/RC3) in the adult and developing oscine song control system

DEVELOPMENTAL NEUROBIOLOGY, Issue 2-3 2009
David F. Clayton
Abstract Songbirds are appreciated for the insights they provide into regulated neural plasticity. Here, we describe the comparative analysis and brain expression of two gene sequences encoding probable regulators of synaptic plasticity in songbirds: neuromodulin (GAP-43) and neurogranin (RC3). Both are members of the calpacitin family and share a distinctive conserved core domain that mediates interactions between calcium, calmodulin, and protein kinase C signaling pathways. Comparative sequence analysis is consistent with known phylogenetic relationships, with songbirds most closely related to chicken and progressively more distant from mammals and fish. The C-terminus of neurogranin is different in birds and mammals, and antibodies to the protein reveal high expression in adult zebra finches in cerebellar Purkinje cells, which has not been observed in other species. RNAs for both proteins are generally abundant in the telencephalon yet markedly reduced in certain nuclei of the song control system in adult canaries and zebra finches: neuromodulin RNA is very low in RA and HVC (relative to the surrounding pallial areas), whereas neurogranin RNA is conspicuously low in Area X (relative to surrounding striatum). In both cases, this selective downregulation develops in the zebra finch during the juvenile song learning period, 25,45 days after hatching. These results suggest molecular parallels to the robust stability of the adult avian song control circuit. © 2008 Wiley Periodicals, Inc. Develop Neurobiol, 2009 [source]

Robust adaptive tracking control of uncertain discrete time systems

INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 9 2005
Shengping Li
Abstract In this paper, the problem of robust adaptive tracking for uncertain discrete-time systems is considered from the slowly varying systems point of view. The class of uncertain discrete-time systems considered is subjected to both ,,, to ,,, bounded unstructured uncertainty and external additive bounded disturbances. A priori knowledge of the dynamic model of the reference signal to be tracked is not completely known. For such problem, an indirect adaptive tracking controller is obtained by frozen-time controllers that at each time optimally robustly stabilize the estimated models of the plant and minimize the worst-case steady-state absolute value of the tracking error of the estimated model over the model uncertainty. Based on ,,, to ,,, stability and performance of slowly varying system found in the literature, the proposed adaptive tracking scheme is shown to have good robust stability. Moreover, a computable upper bound on the size of the unstructured uncertainty permitted by the adaptive system and a computable tight upper bound on asymptotic robust steady-state tracking performance are provided. Copyright © 2005 John Wiley & Sons, Ltd. [source]

On robust stability of uncertain systems with multiple time-delays

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 15 2010
Tong ZhouArticle first published online: 27 NOV 200
Abstract On the basis of an infinite to one mapping and the structure of the null space of a multivariate matrix polynomial (MMP), a novel sufficient condition is derived in this paper for the robust stability of a linear time-invariant system with multiple uncertain time-delays, parametric modelling errors and unmodelled dynamics. This condition depends on time-delay bounds and is less conservative than the existing ones. An attractive property is that this condition becomes also necessary in some physically meaningful situations, such as the case that there is only one uncertain time-delay and neither parametric perturbations nor unmodelling errors exist. Moreover, using ideas of representing a positive-definite MMP through matrix sum of squares, an asymptotic necessary and sufficient condition is derived for the robust stability of this system. All the conditions can be converted to linear matrix inequalities. Copyright © 2009 John Wiley & Sons, Ltd. [source]

On robust control algorithms for nonlinear network consensus protocols

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 3 2010
Qing Hui
Abstract Even though many consensus protocol algorithms have been developed over the last several years in the literature, robustness properties of these algorithms involving nonlinear dynamics have been largely ignored. Robustness here refers to sensitivity of the control algorithm achieving semistability and consensus in the face of model uncertainty. In this paper, we examine the robustness of several control algorithms for network consensus protocols with information model uncertainty of a specified structure. In particular, we develop sufficient conditions for robust stability of control protocol functions involving higher-order perturbation terms that scale in a consistent fashion with respect to a scaling operation on an underlying space with the additional property that the protocol functions can be written as a sum of functions, each homogeneous with respect to a fixed scaling operation, that retain system semistability and consensus. Copyright © 2009 John Wiley & Sons, Ltd. [source]

A test for stability robustness of linear time-varying systems utilizing the linear time-invariant ,-gap metric

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 9 2009
Wynita M. Griggs
Abstract A stability robustness test is developed for internally stable, nominal, linear time-invariant (LTI) feedback systems subject to structured, linear time-varying uncertainty. There exists (in the literature) a necessary and sufficient structured small gain condition that determines robust stability in such cases. In this paper, the structured small gain theorem is utilized to formulate a (sufficient) stability robustness condition in a scaled LTI ,-gap metric framework. The scaled LTI ,-gap metric stability condition is shown to be computable via linear matrix inequality techniques, similar to the structured small gain condition. Apart from a comparison with a generalized robust stability margin as the final part of the stability test, however, the solution algorithm implemented to test the scaled LTI ,-gap metric stability robustness condition is shown to be independent of knowledge about the controller transfer function (as opposed to the LMI feasibility problem associated with the scaled small gain condition which is dependent on knowledge about the controller). Thus, given a nominal plant and a structured uncertainty set, the stability robustness condition presented in this paper provides a single constraint on a controller (in terms of a large enough generalized robust stability margin) that (sufficiently) guarantees to stabilize all plants in the uncertainty set. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Stability and robust stability of positive linear Volterra difference equations

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 5 2009
Pham Huu Anh Ngoc
Abstract We first introduce a class of positive linear Volterra difference equations. Then, we offer explicit criteria for uniform asymptotic stability of positive equations. Furthermore, we get a new Perron,Frobenius theorem for positive linear Volterra difference equations. Finally, we study robust stability of positive equations under structured perturbations and affine perturbations. Two explicit stability bounds with respect to these perturbations are given. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Delay-dependent robust stability for stochastic time-delay systems with polytopic uncertainties

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 15 2008
Hongyi Li
Abstract This paper considers a delay-dependent and parameter-dependent robust stability criterion for stochastic time-delay systems with polytopic uncertainties. The delay-dependent robust stability criterion, as expressed in terms of linear matrix inequalities (LMIs), is obtained by using parameter-dependent Lyapunov functions. It is shown that the result derived by a parameter-dependent Lyapunov functional is less conservative. Numerical examples are provided to illustrate the effectiveness of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Generalization of cluster treatment of characteristic roots for robust stability of multiple time-delayed systems

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 14 2008
Rifat Sipahi
Abstract A new perspective is presented for studying the stability robustness of nth order systems with p rationally independent delays. It deploys a holographic mapping procedure over the delay space into a new coordinate system in order to achieve the objective. This mapping collapses the entire set of potential stability switching points on a manageably small number of hypersurfaces, which are explicitly defined in the new domain. This property considerably alleviates the problem, which is otherwise infinite dimensional, and therefore notoriously complex to handle. We further declare some unrecognized features of these switching hypersurfaces, that they are (a) encapsulated within a higher-dimensional cube with edges of length 2,, which we name the ,building block', and (b) the ,offspring' of this building block, which represent the secondary stability switchings, appear within the adjacent and identical building blocks (cubes) stacked up next to each other. The final outlook is an exclusive representation of stability for this general class of systems at any arbitrary point in the delay space. Two example case studies are also provided, which are not possible to analyze using any other methodology known to the authors. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Delay-range-dependent robust stability and stabilization for uncertain systems with time-varying delay

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 13 2008
Tao Li
Abstract This paper concerns delay-range-dependent robust stability and stabilization for time-delay system with linear fractional form uncertainty. The time delay is assumed to be a time-varying continuous function belonging to a given range. On the basis of a novel Lyapunov,Krasovskii functional, which includes the information of the range, delay-range-dependent stability criteria are established in terms of linear matrix inequality. It is shown that the new criteria can provide less conservative results than some existing ones. Moreover, the stability criteria are also used to design the stabilizing state-feedback controllers. Numerical examples are given to demonstrate the applicability of the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Robust stability of iterative learning control schemes

State-space µ analysis for an experimental drive-by-wire vehicle

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 9 2008
M. Halton
Abstract This paper considers the application of the skewed structured singular value to the robust stability of systems subject to strictly real parametric uncertainty. Three state-space formulations that counteract the discontinuous nature of this problem are detailed. It is shown that the calculation of the supremum of the structured singular value over a frequency range using these formulations transforms into a single skewed structured singular value calculation. Similar to the structured singular value, the exact calculation of the skewed structured singular value is an NP-hard problem. In this work, two efficient algorithms that determine upper and lower bounds on the skewed structured singular value are presented. These algorithms are critically assessed using a series of robustness analysis tests on a safety-critical experimental drive-by-wire vehicle. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Further results on delay-dependent robust stability conditions of uncertain neutral systems

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 5 2005
Shengyuan Xu
Abstract This paper deals with the problem of robust stability analysis for uncertain neutral systems. In terms of a linear matrix inequality (LMI), an improved delay-dependent asymptotic stability criterion is developed without using bounding techniques on the related cross product terms. Based on this, a new delay-dependent LMI condition for robust stability is obtained. Numerical examples are provided to show that the proposed results significantly improve the allowed upper bounds of the delay size over some existing ones in the literature. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Robust stability of neutral systems: a Lyapunov-Krasovskii constructive approach

Robust control from data via uncertainty model sets identification

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 11 2004
S. Malan
Abstract In this paper an integrated robust identification and control design procedure is proposed. The plant to be controlled is supposed to be linear, time invariant, stable, possibly infinite dimensional and a set of noise-corrupted input,output measurements is supposed to be available. The emphasis is placed on the design of controllers guaranteeing robust stability and robust performances, and on the trade-off between controller complexity and achievable robust performances. First, uncertainty models are identified, consisting of parametric models of different order and tight frequency bounds on the magnitude of the unmodelled dynamics. Second, Internal Model Controllers, guaranteeing robust closed-loop stability and best approximating the ,perfect control' ideal target, are designed using H,/,-synthesis techniques. Then, the robust performances of the designed controllers are computed, allowing one to determine the level of model/controller complexity needed to guarantee desired closed-loop performances. Copyright © 2004 John Wiley & Sons, Ltd. [source]

New results for the analysis of linear systems with time-invariant delays

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 12 2003
Jianrong Zhang
Abstract This paper presents a comparison system approach for the analysis of stability and ,, performance of linear time-invariant systems with unknown delays. The comparison system is developed by replacing the delay elements with certain parameter-dependent Padé approximations. It is shown using the special properties of the Padé approximation to e,s that the value sets of these approximations provide outer and inner coverings for that of each delay element and that the robust stability of the outer covering system is a sufficient condition for the stability of the original time delay system. The inner covering system, in turn, is used to provide an upper bound on the degree of conservatism of the delay margin established by the sufficient condition. This upper bound is dependent only upon the Padé approximation order and may be made arbitrarily small. In the single delay case, the delay margin can be calculated explicitly without incurring any additional conservatism. In the general case, this condition can be reduced with some (typically small) conservatism to finite-dimensional LMIs. Finally, this approach is also extended to the analysis of ,, performance for linear time-delay systems with an exogenous disturbance. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Robust nonlinear ship course-keeping control by H, I/O linearization and , -synthesis

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 1 2003
Shr-Shiung Hu
Abstract In this paper, the H, input/output (I/O) linearization formulation is applied to design an inner-loop nonlinear controller for a nonlinear ship course-keeping control problem. Due to the ship motion dynamics are non-minimum phase, it is impossible to use the ordinary feedback I/O linearization to resolve. Hence, the technique of H, I/O linearization is proposed to obtain a nonlinear H, controller such that the compensated nonlinear system approximates the linear reference model in I/O behaviour. Then a , -synthesis method is employed to design an outer-loop robust controller to address tracking, regulation, and robustness issues. The time responses of the tracking signals for the closed-loop system reveal that the overall robust nonlinear controller is able to provide robust stability and robust performance for the plant uncertainties and state measurement errors. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Guaranteed cost inequalities for robust stability and performance analysis

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 15 2002
Dennis S. Bernstein
In this paper, we formulate robust stability and performance bounds in terms of guaranteed cost inequalities. We derive new guaranteed cost bounds for plants with real structured uncertainty, and we reformulate them as linear matrix inequalities (LMIs). In particular, we obtain a shifted linear bound and a shifted inverse bound, and give LMI forms for a shifted bounded real bound, a shifted Popov bound, a shifted linear bound and a shifted inverse bound. Several examples are used to compare the shifted bounds with their unshifted counterparts and to make comparisons among these new bounds and vertex LMI bounds. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Generalization of the Nyquist robust stability margin and its application to systems with real affine parametric uncertainties

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 15 2001
Charles T. Baab
The critical direction theory for analysing the robust stability of uncertain feedback systems is generalized to include the case of non-convex critical value sets, hence making the approach applicable for a much larger class of relevant systems. A redefinition of the critical perturbation radius is introduced, leading to the formulation of a Nyquist robust stability measure that preserves all the properties of the previous theory. The generalized theory is applied to the case of rational systems with an affine uncertainty structure where the uncertain parameters belong to a real rectangular polytope. Necessary and sufficient conditions for robust stability are developed in terms of the feasibility of a tractable linear-equality problem subject to a set of linear inequalities, leading ultimately to a computable Nyquist robust stability margin. A systematic and numerically tractable algorithm is proposed for computing the critical perturbation radius needed for the calculation of the stability margin, and the approach is illustrated via examples. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Robust stability and structured uncertainty bounded by the Euclidean norm

Simultaneous Automatic Control of Oxygen and Carbon Dioxide Blood Gases During Cardiopulmonary Bypass

ARTIFICIAL ORGANS, Issue 6 2010
Berno J.E. Misgeld
Abstract In this work an automatic control strategy is presented for the simultaneous control of oxygen and carbon dioxide blood gas partial pressures to be used during cardiopulmonary bypass surgery with heart,lung machine support. As the exchange of blood gases in the artificial extracorporeal lung is a highly nonlinear process comprising varying time delays, uncertainties, and time-varying parameters, it is currently being controlled manually by specially trained perfusionist staff. The new control strategy includes a feedback linearization routine with augmented time-delay compensation and two external linear gain-scheduled controllers, for partial oxygen and carbon dioxide pressures. The controllers were robustly tuned and tested in simulations with a detailed artificial lung (oxygenator) model in cardiopulmonary bypass conditions. Furthermore, the controllers were implemented in an ex vivo experiment using fresh porcine blood as a substitute fluid and a special deoxygenation technique to simulate a patient undergoing cardiopulmonary bypass. Both controllers showed robust stability during the experiments and a good disturbance rejection to extracorporeal blood flow changes. This automatic control strategy is proposed to improve patient's safety by fast control reference tracking and good disturbance rejection under varying conditions. [source]

Robust stabilization for uncertain discrete singular time-delay systems,

ASIAN JOURNAL OF CONTROL, Issue 2 2010
Xiaofu Ji
Abstract The problem of robust stabilization for uncertain discrete singular time-delay systems is investigated. The considered systems are subject to norm-bounded parameter uncertainties and constant time delay. A linear matrix inequality (LMI) condition is proposed for a discrete singular time-delay system to be regular, causal and stable. With this condition, the problems of robust stability and stabilization are solved. The obtained results are formulated in terms of strict LMIs. An explicit expression of the desired state-feedback control law is also given, which involves no matrix decomposition. The proposed synthesis method is illustrated by a numerical example. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source]

Delay-dependent robust stability and stabilization for uncertain discrete singular systems with delays ,,

ASIAN JOURNAL OF CONTROL, Issue 3 2009
Shuping Ma
Abstract The robust stability and robust stabilization for time-delay discrete singular systems with parameter uncertainties is discussed. A delay-dependent linear matrix inequality (LMI) condition for the time-delay discrete systems to be nonsingular and stable is given. Based on this condition and the restricted system equivalent transformation, the delay-dependent LMI condition is proposed for the time-delay discrete singular systems to be admissible. With this condition, the problems of robust stability and robust stabilization are solved, and the delay-dependent LMI conditions are obtained. Numerical examples illustrate the effectiveness of the method given in the paper. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source]