Robust stability and stabilizability of uncertain linear hybrid systems with state delays

Phát, Vũ Ngọc

doi:10.1109/tcsii.2004.840115

Cited by 55 publications

(38 citation statements)

References 14 publications

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“…It should be pointed out that introduction of (9), (10) and (17) helps exploit the structure of diffusion of the system and deal with the crossing terms. This leads to a less conservative result.…”

Section: Resultsmentioning

confidence: 99%

Section: X(t) = A(r(t))x(t) mentioning

confidence: 99%

“…Over the past decades, a great deal of attention has been devoted the study of this class of systems (see, e.g., [10], [2], [11] and [15]). Since time delays and uncertainties often appear in practical systems and may induce poor performance and instability, uncertain jump linear systems with time delays have also been studied by many authors (see [10]- [17]). Furthermore, if r(t) is a Markovian chain and environmental noise is taken into account as well as time delay and uncertainty, the system becomes a stochastic delay system with Markovian switching (1), also called a hybrid stochastic delay system (see, e.g., [7]).…”

Section: X(t) = A(r(t))x(t) mentioning

confidence: 99%

“…f (r(s), s)ds + g(r(s), s)dw(s) (10) for all i ∈ S and t ≥ h. Choose a Lyapunov-Krasovskii functional candidate for system (7) as follows:…”

Section: Problem Statementmentioning

confidence: 99%

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Delay-dependent robust stability of stochastic delay systems with Markovian switching

Huang

Mao

Deng

2009

J. Control Theory Appl.

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This version is available at https://strathprints.strath.ac.uk/16872/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Abstract: In recent years, stability of hybrid stochastic delay systems, one of the important issues in the study of stochastic systems, has received considerable attention. However, the existing results do not deal with the structure of the diffusion but estimate its upper bound, which induces conservatism. This paper studies delay-dependent robust stability of hybrid stochastic delay systems. A delay-dependent criterion for robust exponential stability of hybrid stochastic delay systems is presented in terms of linear matrix inequalities (LMIs), which exploits the structure of the diffusion. Numerical examples are given to verify the effectiveness and less conservativeness of the proposed method.

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Section: Resultsmentioning

confidence: 99%

Section: X(t) = A(r(t))x(t) mentioning

confidence: 99%

Section: X(t) = A(r(t))x(t) mentioning

confidence: 99%

“…f (r(s), s)ds + g(r(s), s)dw(s) (10) for all i ∈ S and t ≥ h. Choose a Lyapunov-Krasovskii functional candidate for system (7) as follows:…”

Section: Problem Statementmentioning

confidence: 99%

See 2 more Smart Citations

Delay-dependent robust stability of stochastic delay systems with Markovian switching

Huang

Mao

Deng

2009

J. Control Theory Appl.

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“…The stabilization problem of arbitrary switched linear systems with unknown time varying delays was considered in Hetel, Daafouz & Iung (2006). For uncertain linear discrete-time switched systems with state delays, sufficient conditions of robust stability and stabilizability in terms of matrix inequalities and Riccati-like inequalities were given in Phat (2005). Stability of a class of switched delay systems was shown in Kim Campbell & Liu (2006) by using a common Lyapunov functional method.…”

Section: Introduction *mentioning

confidence: 99%

Robust Control of Uncertain Switched Delay Systems: a Sliding Mode Control Design

Lian

Dimirovski

Zhao

2008

IFAC Proceedings Volumes

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This paper investigates the robust sliding mode control problem for a class of uncertain switched delay systems. A single sliding surface is constructed such that the reduced-order equivalent sliding motion restricted to the sliding surface is completely invariant to all admissible uncertainties. For the cases of known delay and unknown delay, the existence conditions of the sliding surface are proposed, respectively. The corresponding hysteresis switching laws are designed to asymptotically stabilize the sliding motion. Furthermore, variable structure controllers are developed to drive the state of the switched system to reach the single sliding surface in finite time and remain on it thereafter. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

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Robust Stability Criterion for Discrete‐Time Nonlinear Switched Systems with Randomly Occurring Delays via T–S Fuzzy Approach

Balasubramaniam

Banu

2014

Complexity

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This article investigates exponential stability of uncertain discrete‐time nonlinear switched systems with parameter uncertainties and randomly occurring delays via Takagi–Sugeno fuzzy approach. The randomness of time‐varying delay is characterized by introducing a Bernoulli stochastic variable that follows certain probability distribution. By adopting the average dwell‐time approach with Lyapunov–Krasovskii functional and using convex reciprocal lemma, delay‐dependent sufficient conditions for exponential stability of the switched fuzzy system are derived in terms of linear matrix inequalities (LMIs), which can be solved readily using any LMI solvers. Finally, illustrative examples are provided to demonstrate the effectiveness of the proposed approach. © 2014 Wiley Periodicals, Inc. Complexity 20: 49–61, 2015

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Robust stability and stabilizability of uncertain linear hybrid systems with state delays

Cited by 55 publications

References 14 publications

Delay-dependent robust stability of stochastic delay systems with Markovian switching

Delay-dependent robust stability of stochastic delay systems with Markovian switching

Robust Control of Uncertain Switched Delay Systems: a Sliding Mode Control Design

Robust Stability Criterion for Discrete‐Time Nonlinear Switched Systems with Randomly Occurring Delays via T–S Fuzzy Approach

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