Stabilization of switched linear systems via admissible edge-dependent switching signals

Yang, Junqi; Zhao, Xudong; Bu, Xuhui; Qian, Wei

doi:10.1016/j.nahs.2018.01.003

Cited by 71 publications

(33 citation statements)

References 32 publications

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“…Three numerical examples with some comparisons between the latest results are presented to show the validity and superiority of the developed techniques. It is worth mentioning that, recently, some extended versions of MDADT were proposed such as edge-dependent ADT 29,30 and mode-mode-dependent ADT. 31 How to develop the ideas and methods of this paper to these new concepts is a worthy research direction.…”

Section: Resultsmentioning

confidence: 99%

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A limit inferior ‐dependent average dwell time approach for stability analysis of switched systems

Zhai

2020

Intl J Robust & Nonlinear

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A novel concept of limit inferior Φ-dependent average dwell time (LΦDADT) is first proposed, which is a generalization of various existing concepts of dwell time. Based on the LΦDADT scheme and the multiple Lyapunov function approach, some new sufficient conditions for stability and stabilization of switched systems are established by introducing some inequalities. Those criteria acquired contain most of the established ones based on ADT, limiting ADT, mode-dependent ADT, Φ-dependent ADT, etc. Specifically, the stability and stabilization criteria for switched linear systems are listed as linear matrix inequalities that can be examined and calculated easily by the LMI toolbox in Matlab. At last, three typical numerical examples are presented for illustrating the effectiveness and validity of the LΦDADT scheme presented in this paper.

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Section: Resultsmentioning

confidence: 99%

“…Consider the Lyapunov candidate function V (t) (x(t)) = x T (t)X −1 (t) x(t) for the system (29). Without loss of generality, suppose t ∈ [t k , t k + 1 ) and (t…”

Section: Theorem 2 (Stability With Practicality Under Lφdadt) Considmentioning

confidence: 99%

A limit inferior ‐dependent average dwell time approach for stability analysis of switched systems

Zhai

2020

Intl J Robust & Nonlinear

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“…The set of ATEs is denoted by

scriptA

. An ATE

ε false(p, q false)

has an ATE‐dependent weight (ATEW)

μ_{p, q}

, which describes the switching property from p to q and will be given later, and the set of ATEWs is signified by

scriptW

[23].…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

“…Further reports, such as

H_{\infty}

control for 2D switched systems [19], observer‐based sliding mode control of switched positive non‐linear systems [20], control design of positive switched systems [21], and

H_{\infty}

fixed‐order filtering for linear parameter‐varying (LPV) switched delay systems [22], have been given with MDADT under asynchronous switching control. Recently, by virtue of different transition edges, an novel admissible edge‐dependent ADT (AED‐ADT) switching motion is formulated in [23], which generalises the MDADT regime and further relaxes its restrictions. Then a

H_{\infty}

control problem for discrete‐time switched systems is investigated via the AED‐ADT method [24].…”

Section: Introductionmentioning

confidence: 99%

Asynchronously switching control for a class of switched neutral systems: a novel discontinuous Lyapunov function approach

Wang

Zhang

2020

IET Control Theory & Appl

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“…More and more attention has been devoted to these stochastic hybrid systems. [10][11][12] Markov switching systems, as a special class of hybrid system, have also been broadly investigated. The switching between different operation modes is governed by a feasible continuous-time Markov chain as shown in Reference 13.…”

Section: Introductionmentioning

confidence: 99%

Boundary control of stochastic reaction‐diffusion systems with Markovian switching

Han

Ding

et al. 2020

Intl J Robust & Nonlinear

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This article focuses on the boundary control of stochastic Markovian reaction-diffusion systems (SMRDSs). Both the cases of completely known and partially unknown transition probabilities are taken into account. By using the Lyapunov functional method, a sufficient condition is obtained under the designed boundary controllers to guarantee the asymptotic mean square stability for SMRDSs with completely known transition probabilities. For the case of partially unknown transition probabilities, we introduce free-connection weighting matrices to handle the boundary control problem. When external disturbance enters the system, a sufficient criterion of H-infinity boundary control is developed. Furthermore, robust stabilization is investigated for parametric uncertain SMRDSs in both cases. Two examples are presented to demonstrate the efficiency of the proposed approaches. K E Y W O R D S asymptotic stability, boundary control, H-infinity control, partially unknown transition probabilities, stochastic Markovian reaction-diffusion systems Int J Robust Nonlinear Control. 2020;30:4129-4148.wileyonlinelibrary.com/journal/rnc

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Stabilization of switched linear systems via admissible edge-dependent switching signals

Cited by 71 publications

References 32 publications

A limit inferior ‐dependent average dwell time approach for stability analysis of switched systems

A limit inferior ‐dependent average dwell time approach for stability analysis of switched systems

Asynchronously switching control for a class of switched neutral systems: a novel discontinuous Lyapunov function approach

Boundary control of stochastic reaction‐diffusion systems with Markovian switching

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