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Matrix Inequalities (matrix + inequality)

Distribution by Scientific Domains
Engineering96%
Chemistry3%

Kinds of Matrix Inequalities

  • linear matrix inequality
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  • strict linear matrix inequality
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    Terms modified by Matrix Inequalities

  • matrix inequality approach
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    Selected Abstracts

    An LMI approach to design observer for unknown inputs Takagi-Sugeno fuzzy models

    ASIAN JOURNAL OF CONTROL, Issue 4 2010
    M. Chadli
    Abstract This paper considers the design of an observer for a Takagi-Sugeno (T-S) fuzzy model subject to unknown inputs affecting states and outputs of the system simultaneously. Uncertainties affecting state matrices are also considered. Based on the Lyapunov method, sufficient conditions in Linear Matrix Inequalities (LMI) terms are proposed to design the given unknown input T-S observer. In order to improve the performances of the proposed T-S observer, the pole placement in an LMI region is also considered. An numerical example is given to illustrate the validity of the derived results. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source]

    Construction of Lyapunov function for power system based on solving linear matrix inequality

    ELECTRICAL ENGINEERING IN JAPAN, Issue 4 2007
    Atsushi Ishigame
    Abstract This paper presents construction of Lyapunov functions for power systems based on solving the Linear Matrix Inequality (LMI) derived from the Lyapunov stability theorem considering the dynamics of load characteristic and AVR control system. The proposed Lyapunov function is constructed as a quadratic form of state variables and an integral term which satisfies the curl equation and the sector condition. An induction machine and a synchronous machine are considered as load characteristics. One-machine one-load infinite bus system is considered taking into account the flux decay effects and AVR with one time constant of the generator. To verify the proposed Lyapunov function, the transient stability assessment is shown. The critical clearing times given by the proposed Lyapunov function are compared with those obtained by the numerical integration method, and they are shown to be practical. © 2007 Wiley Periodicals, Inc. Electr Eng Jpn, 158(4): 42, 50, 2007; Published online in Wiley InterScience (www.interscience. wiley.com). DOI 10.1002/eej.20328 [source]

    Tracking control for switched linear systems with time-delay: a state-dependent switching method,

    ASIAN JOURNAL OF CONTROL, Issue 5 2009
    Qing-Kui Li
    Abstract Tracking control for switched linear systems with time-delay is investigated in this paper. Based on the state-dependent switching method, sufficient conditions for the solvability of the tracking control problem are given. We use single Lyapunov function technique and a typical hysteresis switching law to design a tracking control law such that the H, model reference tracking performance is satisfied. The controller design problem can be solved efficiently by using linear matrices inequalities. Since convex combination techniques are used to derive the delay independent criteria, some subsystems are allowed to be unstable. It is highly desirable that a non-switched time-delay system can not earn such property. Simulation example shows the feasibility and validity of the switching control law. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source]

    Neural-network-based finite-time H, control for extended Markov jump nonlinear systems

    INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 7 2010
    Xiaoli Luan
    Abstract This paper presents a neural-network-based finite-time H, control design technique for a class of extended Markov jump nonlinear systems. The considered stochastic character is described by a Markov process, but with only partially known transition jump rates. The sufficient conditions for the existence of the desired controller are derived in terms of linear matrix inequalities such that the closed-loop system trajectory stays within a prescribed bound in a fixed time interval and has a guaranteed H, noise attenuation performance for all admissible uncertainties and approximation errors of the neural networks. A numerical example is used to illustrate the effectiveness of the developed theoretic results. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    Passification-based adaptive control of linear systems: Robustness issues

    INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 6 2008
    Dimitri Peaucelle
    Abstract Passivity is a widely used concept in control theory having led to many significant results. This paper concentrates on one characteristic of passivity, namely passification-based adaptive control. This concept applies to multi-input multi-output systems for which exists a combination of outputs that renders the open-loop system hyper-minimum phase. Under such assumptions, the system may be passified by both high-gain static output feedback and by a particular adaptive control algorithm. This last control law is modified here to guarantee its coefficients to be bounded. The contribution of this paper is to investigate its robustness with respect to parametric uncertainty. Time response characteristics are illustrated on examples including realistic situations with noisy output and saturated input. Theoretical results are formulated as linear matrix inequalities and can hence be readily solved with semi-definite programming solvers. Copyright © 2007 John Wiley & Sons, Ltd. [source]

    Robust H, filtering for switched linear discrete-time systems with polytopic uncertainties

    INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 6 2006
    Lixian 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]

    Exponential convergence of the Kalman filter based parameter estimation algorithm

    INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 10 2003
    Liyu Cao
    Abstract In this paper we shall present a new method to analyse the convergence property of the Kalman filter based parameter estimation algorithms. This method for convergence analysis is mainly based on some matrix inequalities and is more simple than some of the existing approaches in the literature. This method can simultaneously provide both lower and upper bounds on the exponential convergence rate as the functions of bounds of the related matrices, such as the covariance matrices. A simulation example is provided to illustrate the convergence property of the Kalman filter based algorithms. Copyright © 2003 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]

    Robust control of T-S fuzzy systems with time-varying delay using new approach

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 14 2010
    Hamdi Gassara
    Abstract This paper aims to design a controller to robustly stabilize uncertain nonlinear systems with time-varying delay and norm bounded uncertainties via Takagi,Sugeno (T-S) fuzzy model. The stabilization conditions are given in the form of linear matrix inequalities using a single Lyapunov,Krasovskii functional (LKF) combining the introduction of some relaxation matrices and only one tuning parameter. In comparison with the existing techniques in the literature, the proposed approach has two major advantages. The first is the reduction of computational complexity when the number of IF-THEN rules, r, is big. The second concerns the conservatism reduction. Several examples are given to show the effectiveness and the merits of the design procedure. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    Delay-dependent robust control for singular discrete-time Markovian jump systems with time-varying delay

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 10 2010
    Wuneng Zhou
    Abstract The problem of delay-dependent robust stabilization for uncertain singular discrete-time systems with Markovian jumping parameters and time-varying delay is investigated. In terms of free-weighting-matrix approach and linear matrix inequalities, a delay-dependent condition is presented to ensure a singular discrete-time system to be regular, causal and stochastically stable based on which the stability analysis and robust stabilization problem are studied. An explicit expression for the desired state-feedback controller is also given. Some numerical examples are provided to demonstrate the effectiveness of the proposed approach. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    Robust fault detection and isolation for parameter-dependent LFT systems

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 7 2010
    Xuejing Cai
    Abstract In this paper, we consider robust fault detection and isolation (FDI) problems for faulty linear systems with linear fractional transformation (LFT) parameter dependency and propose an observer-based solution by using multiobjective optimization techniques. To simplify the design process, a general faulty LFT system will be constructed from the standard LFT description by converting actuator/system component faults into sensor faults first. Then a bank of parameter-dependent FDI filters will be designed to identify each fault. Each FDI filter will generate a residual signal to track an individual fault with minimum error and to suppress the effects of disturbances, time-varying parameters and other fault signals. The design of LFT parameter-dependent FDI filters, as a multiobjective optimization problem, will be formulated in terms of linear matrix inequalities (LMIs) and can be solved efficiently. A numerical example is used to demonstrate the proposed fault detection and isolation approach for LFT systems with different parametric structures. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    New absolute stability criteria for time-delay Lur'e systems with sector-bounded nonlinearity

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 6 2010
    Xian Liu
    Abstract This paper is concerned with the problem of absolute stability of time-delay Lur'e systems with sector-bounded nonlinearity. Several novel criteria are presented by using a Lur'e,Postnikov function. For a general Lur'e system with known time delay, the absolute stability of it is analyzed by solving a set of linear matrix inequalities (LMIs). The maximum upper bound of the allowable time delay for a general Lur'e system is derived by solving a convex optimization problem. The feasibility of the LMIs implies some frequency-domain interpretations which are similar to the frequency-domain inequalities in the circle criterion and the Popov criterion. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    Stability and stabilization of discrete-time singular Markov jump systems with time-varying delay

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 5 2010
    Shuping Ma
    Abstract The stochastic stability and stochastic stabilization of time-varying delay discrete-time singular Markov jump systems are discussed. For full and partial knowledge of transition probabilities cases, delay-dependent linear matrix inequalities (LMIs) conditions for the systems to be regular, causal and stochastically stable are given. Sufficient conditions are proposed for the existence of state feedback controller in terms of LMIs. Finally, two numerical examples to illustrate the effectiveness of the method are given. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    An augmented system approach to static output-feedback stabilization with ,, performance for continuous-time plants

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 7 2009
    Zhan Shu
    Abstract This paper revisits the static output-feedback stabilization problem of continuous-time linear systems from a novel perspective. The closed-loop system is represented in an augmented form, which facilitates the parametrization of the controller matrix. Then, new equivalent characterizations on stability and ,, performance of the closed-loop system are established in terms of matrix inequalities. On the basis of these characterizations, a necessary and sufficient condition with slack matrices for output-feedback stabilizability is proposed, and an iteration algorithm is given to solve the condition. An extension to output-feedback ,, control is provided as well. The effectiveness and merits of the proposed approach are shown through several examples. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Observer design with guaranteed RMS gain for discrete-time LPV systems with Markovian jumps

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 6 2009
    Giuseppe C. Calafiore
    Abstract In this paper we consider the problem of designing state observers with guaranteed power-to-power (RMS) gain for a class of stochastic discrete-time linear systems that possess both measurable parameter variations and Markovian jumps in their dynamics. It is shown in the paper that an upper bound on the RMS gain of the observer can be characterized in terms of feasibility of a family of parameter-dependent linear matrix inequalities (LMIs). Any feasible solution to these LMIs can then be used to explicitly construct a parameter-varying jump observer that guarantees the desired performance level. This design framework is then specialized to a problem of state estimation for a linear parameter-varying plant whose state measurements are available through a lossy Bernoulli channel. Two numerical examples illustrate the results. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Exponential H, filtering for switched linear systems with interval time-varying delay

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 5 2009
    Dong Wang
    Abstract This paper deals with the problem of exponential H, filtering for a class of continuous-time switched linear system with interval time-varying delay. The time delay under consideration includes two cases: one is that the time delay is differentiable and bounded with a constant delay-derivative bound, whereas the other is that the time delay is continuous and bounded. Switched linear filters are designed to ensure that the filtering error systems under switching signal with average dwell time are exponentially stable with a prescribed H, noise attenuation level. Based on the free-weighting matrix approach and the average dwell technology, delay-dependent sufficient conditions for the existence of such a filter are derived and formulated in terms of linear matrix inequalities (LMIs). By solving that corresponding LMIs, the desired filter parameterized matrices and the minimal average dwell time are obtained. Finally, two numerical examples are presented to demonstrate the effectiveness of the developed results. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Network-based H, control for stochastic systems

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 3 2009
    Xiangyu Meng
    Abstract This paper investigates the problem of network-based control for stochastic plants. A new model of stochastic time-delay systems is presented where both network-induced delays and packet dropouts are taken into consideration for a sampled-data network-based control system. This model consists of two successive delay components in the state, and we solve the network-based H, control problem based on this model by a new stochastic delay system approach. The controller design for the sampled-data systems is carried out in terms of linear matrix inequalities. Finally, we illustrate the methodology by applying these results to an air vehicle control problem. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    LMI optimization approach to robust H, observer design and static output feedback stabilization for discrete-time nonlinear uncertain systems

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 3 2009
    Masoud Abbaszadeh
    Abstract A new approach for the design of robust H, observers for a class of Lipschitz nonlinear systems with time-varying uncertainties is proposed based on linear matrix inequalities (LMIs). The admissible Lipschitz constant of the system and the disturbance attenuation level are maximized simultaneously through convex multiobjective optimization. The resulting H, observer guarantees asymptotic stability of the estimation error dynamics and is robust against nonlinear additive uncertainty and time-varying parametric uncertainties. Explicit norm-wise and element-wise bounds on the tolerable nonlinear uncertainty are derived. Also, a new method for the robust output feedback stabilization with H, performance for a class of uncertain nonlinear systems is proposed. Our solution is based on a noniterative LMI optimization and is less restrictive than the existing solutions. The bounds on the nonlinear uncertainty and multiobjective optimization obtained for the observer are also applicable to the proposed static output feedback stabilizing controller. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Integrated fault detection and control for LPV systems

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 3 2009
    Heng Wang
    Abstract This paper studies the integrated fault detection and control problem for linear parameter-varying systems. A parameter-dependent detector/controller is designed to generate two signals: residual and control signals that are used to detect faults and simultaneously meet some control objectives. The low-frequency faults and certain finite-frequency disturbances are considered. With the aid of the newly developed linearization techniques, the design methods are presented in terms of solutions to a set of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed methods. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Controlling Chua's circuits using computational verb controllers

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 17 2008
    R. Tonelli
    Abstract In this paper, computational verb controllers were used to control Chua's circuits that were chaotic. The computational verb rule-wise linear models of Chua's circuits were used to approximately segment the dynamics of Chua's circuits into four qualitatively different clusters; namely, the dynamics in the inner region, in the outer region and at boundaries of both regions. Then the stable verb controllers were designed by using linear matrix inequalities. Simulation results are presented to show the soundness of the design method. 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]

    Guaranteed cost control of T,S fuzzy systems with input delay

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 12 2008
    Bing Chen
    Abstract This paper is concerned with the problem of guaranteed cost control for Takagi,Sugeno (T,S) fuzzy systems with time-varying input delay. The input delay is of interval type, and no restriction is imposed on the derivative of the time delay. Based on free-weighting matrix method, new delay-dependent sufficient conditions for the existence of a fuzzy guaranteed cost controller are provided by means of linear matrix inequalities. Some examples are used to illustrate the effectiveness of the proposed method. Copyright © 2007 John Wiley & Sons, Ltd. [source]

    Exponential H, filtering for uncertain discrete-time switched linear systems with average dwell time: A µ-dependent approach

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 11 2008
    Lixian Zhang
    Abstract In this paper, the problem of exponential H, filter problem for a class of discrete-time polytopic uncertain switched linear systems with average dwell time switching is investigated. The exponential stability result of the general discrete-time switched systems using a discontinuous piecewise Lyapunov function approach is first explored. Then, a new µ- dependent approach is proposed, which means the analysis or synthesis of the underlying systems is dependent on the increase degree µ of the piecewise Lyapunov function at the switching instants. A mode-dependent full-order filter is designed such that the developed filter error system is robustly exponentially stable and achieves an exponential H, performance. Sufficient existence conditions for the desired filter are derived and formulated in terms of a set of linear matrix inequalities, and consequently the minimal average dwell time and the corresponding filter are obtained from such conditions for a given system decay degree. A numerical example is presented to demonstrate the potential and effectiveness of the developed theoretical results. Copyright © 2007 John Wiley & Sons, Ltd. [source]

    Robust absolute stability criteria for uncertain Lur'e systems of neutral type

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 3 2008
    Qing-Long Han
    Abstract This paper is concerned with robust absolute stability of uncertain Lur'e systems of neutral type. Some delay-dependent stability criteria are obtained and formulated in the form of linear matrix inequalities. The criteria cover some existing results as their special cases. Neither model transformation nor bounding technique for cross terms is involved through derivation of the stability criteria. Numerical examples show the effectiveness of the criteria. Copyright © 2007 John Wiley & Sons, Ltd. [source]

    Simultaneous ,2/,, control of uncertain jump systems with functional time-delays

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 3 2008
    Magdi S. Mahmoud
    Abstract This paper presents new results pertaining to the control design of a class of linear uncertain systems with Markovian jump parameters. An integral part of the system dynamics is a delayed state in which the time-delays are mode dependent. The jumping parameters are modelled as a continuous-time, discrete-state Markov process and the uncertainties are norm-bounded. We construct an appropriate Lyapunov,Krasovskii functional and design a simultaneous ,2/,, controller which minimizes a quadratic ,2 performance measure while satisfying a prescribed ,, -norm bound on the closed-loop system. It is established that sufficient conditions for the existence of the simultaneous ,2/,, controller and the associated performance upper bound are cast in the form of linear matrix inequalities. Simulation results are provided and extension to the case where the jumping rates are subject to uncertainties is presented. Copyright © 2007 John Wiley & Sons, Ltd. [source]

    On delay-dependent LMI-based guaranteed cost control of uncertain neutral systems with discrete and distributed time-varying delays

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 12 2007
    Jenq-Der Chen
    Abstract In this paper, the problem of designing robust guaranteed cost control law for a class of uncertain neutral system with a given quadratic cost function is considered. Based on Lyapunov,Krasovskii functional theory, a delay-dependent criterion for the existence of guaranteed cost controller is expressed in the form of two linear matrix inequalities (LMIs), which can be solved by using effective LMI toolbox. Moreover, a convex optimization problem satisfying some LMI constraints is formulated to solve a guaranteed cost controller which achieves the minimization of the closed-loop guaranteed cost. An efficient approach is proposed to design the guaranteed cost control for uncertain neutral systems. Computer software Matlab can be used to solve all the proposed results. Finally, a numerical example is illustrated to show the usefulness of our obtained design method. Copyright © 2006 John Wiley & Sons, Ltd. [source]

    A sliding mode control approach for systems subjected to a norm-bounded uncertainty

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 4 2007
    Anis Sellami
    Abstract This paper proposes a design approach of continuous sliding mode control of uncertain systems, the uncertainty being norm bounded. The two steps of the design methodology are investigated. The existence step, in which we choose the sliding surface that gives good behaviour during the sliding mode, is formulated as a pole assignment of linear uncertain system in a sector through convex optimization. The solution to this problem is therefore numerically tractable via linear matrix inequalities (LMI) optimization. In the reaching step, we propose a continuous nonlinear control strategy ensuring a bounded motion about the ideal sliding mode, thus approximating the ideal dynamic behaviour in the presence of uncertainty. Finally, the validity and the applicability of this approach are illustrated by a flight stabilization benchmark example. Copyright © 2006 John Wiley & Sons, Ltd. [source]

    Delay-dependent fault estimation for uncertain time-delay nonlinear systems: an LMI approach

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 18 2006
    Sing Kiong Nguang
    Abstract This paper deals with the problem of robust fault estimation for uncertain time-delay Takagi,Sugeno (TS) fuzzy models. The aim of this study is to design a delay-dependent fault estimator ensuring a prescribed ,, performance level for the fault estimation error, irrespective of the uncertainties and the time delays. Sufficient conditions for the existence of a robust fault estimator are given in terms of linear matrix inequalities (LMIs). Membership functions' (MFs) characteristics are incorporated into the fault estimator design to reduce the conservativeness of neglecting these characteristics. Finally, a numerical example is given to illustrate the effectiveness of the proposed design techniques. Copyright © 2006 John Wiley & Sons, Ltd. [source]

    Gain-scheduled H, filtering of parameter-varying systems

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 8 2006
    Shaosheng Zhou
    Abstract This paper deals with the gain-scheduled H, filtering problem for a class of parameter-varying systems. A sufficient condition for the existence of a gain-scheduled filter, which guarantees the asymptotic stability with an H, noise attenuation level bound for the filtering error system, is given in terms of a finite number of linear matrix inequalities (LMIs). The filter is designed to be parameter-varying and have a nonlinear fractional transformation structure. A numerical example is presented to demonstrate the application of the proposed method. Copyright © 2006 John Wiley & Sons, Ltd. [source]

    Exponential estimates for neutral time delay systems with multiple delays

    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 2 2006
    Vladimir Kharitonov
    Abstract Exponential estimates and sufficient conditions for the exponential stability of linear neutral time delay for systems with multiple delays are given. The case of systems with uncertainties, including uncertainties in the difference operator, is considered. The proofs follows from new results on non-homogeneous difference equations evolving in continuous time combined with the Lyapunov,Krasovskii functionals approach. The conditions are expressed in terms of linear matrix inequalities. The particular case of neutral time delay systems with commensurate delays, which leads to less restrictive exponential estimates, is also addressed. Copyright © 2005 John Wiley & Sons, Ltd. [source]