Robust ℋ ℋ∞ filtering for polytopic uncertain systems via convex optimisation

Jin, Seung Hee; Park, J.B.

doi:10.1049/ip-cta:20010237

Cited by 69 publications

(40 citation statements)

References 13 publications

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“…As shown in Reference [31], the polytopic type uncertainty in (4) can be used to describe the parametric uncertainty more precisely, and cover wider classes of uncertainties than the normbounded uncertainty. In fact, (4) is a generalization of the so-called matching condition.…”

Section: Remarkmentioning

confidence: 99%

RobustH∞ filtering for switched linear discrete-time systems with polytopic uncertainties

Zhang

Shi

Wang

et al. 2006

Int. J. Adapt. Control Signal Process.

150

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In this paper, the problem of robust H 1 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 1 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 1 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.

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Section: Remarkmentioning

confidence: 99%

RobustH∞ filtering for switched linear discrete-time systems with polytopic uncertainties

Zhang

Shi

Wang

et al. 2006

Int. J. Adapt. Control Signal Process.

150

View full text Add to dashboard Cite

show abstract

“…As shown in [23], the polytopic type uncertainty in (2) can be used to describe the parametric uncertainty more precisely, and cover wider classes of uncertainties than the norm-bounded 1191 uncertainty. Note that the parameters and the structure of the uncertainties in practice are usually the same throughout either the multi-models or switched control systems [24,25].…”

Section: Remarkmentioning

confidence: 99%

Exponential H_∞ filtering for uncertain discrete‐time switched linear systems with average dwell time: A µ‐dependent approach

Zhang

Boukas

Shi

2007

Intl J Robust & Nonlinear

196

159

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SUMMARYIn 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 -dependent approach is proposed, which means the analysis or synthesis of the underlying systems is dependent on the increase degree 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.

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“…Then, the robust H ∞ filtering problem to be addressed in this paper can be formulated as follows: given the uncertain discrete-time stochastic delay system ( ) and a prescribed level of noise attenuation γ > 0, determine a stochastically stable filter ( f ) in the form of (10) and (11) such that the filtering error system (˜ ) is stochastically stable, and under zero initial conditions,…”

Section: Problem Formulationmentioning

confidence: 99%

“…Various approaches have been proposed in dealing with the H ∞ filtering problem, and numerous results have been reported in the literature; see, e.g., [1], [12], [14], and the references therein. The robust H ∞ filtering problem has been investigated recently for the case when parameter uncertainties appear in a dynamic system [11].…”

Section: Introductionmentioning

confidence: 99%

Robust H∞ Filtering for Uncertain Discrete Stochastic Systems with Time Delays

Lam

Gao

et al. 2005

Circuits Syst Signal Process

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This paper considers the problem of robust H ∞ filtering for uncertain discretetime stochastic systems with time-varying delays. The parameter uncertainties are assumed to be real time-varying norm-bounded in both the state and measurement equations. The problem to be addressed is the design of a stable filter that guarantees stochastic stability and a prescribed H ∞ performance level of the filtering error system for all admissible uncertainties and time delays. A sufficient condition for the existence of such filters is obtained in terms of a linear matrix inequality (LMI). For the case when this LMI is feasible, an explicit expression for a desired filter is given. An illustrative example is also provided to demonstrate the effectiveness and applicability of the proposed method.

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Robust ℋ ℋ∞ filtering for polytopic uncertain systems via convex optimisation

Cited by 69 publications

References 13 publications

RobustH∞ filtering for switched linear discrete-time systems with polytopic uncertainties

RobustH∞ filtering for switched linear discrete-time systems with polytopic uncertainties

Exponential H_∞ filtering for uncertain discrete‐time switched linear systems with average dwell time: A µ‐dependent approach

Robust H∞ Filtering for Uncertain Discrete Stochastic Systems with Time Delays

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Robust ℋ ℋ∞ filtering for polytopic uncertain systems via convex optimisation

Cited by 69 publications

References 13 publications

RobustH∞ filtering for switched linear discrete-time systems with polytopic uncertainties

RobustH∞ filtering for switched linear discrete-time systems with polytopic uncertainties

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

Robust H∞ Filtering for Uncertain Discrete Stochastic Systems with Time Delays

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Exponential H_∞ filtering for uncertain discrete‐time switched linear systems with average dwell time: A µ‐dependent approach