Switching signal design for exponential stability of discrete switched systems with interval time-varying delay

Lien, Chang‐Hua; Yu, Ker‐Wei; Chang, Hao‐Chin; Chung, Long-Yeu; Chen, Jenq-Der

doi:10.1016/j.jfranklin.2012.04.001

Cited by 15 publications

(9 citation statements)

References 25 publications

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“…In this section, we consider some numerical examples in [26,27] to show that the proposed theorem in this paper provides less conservativeness with comparison to some existing results.…”

Section: Examplesmentioning

confidence: 99%

“…During the last two decades, much attention has been paid to the problem of stability analysis and controller synthesis for time-delay systems (see, e.g., [15][16][17][18]). A switched system with time-delay individual subsystems is called a switched time-delay system [19][20][21][22][23][24][25][26][27][28]. Switched time-delay systems have various applications in practical engineering systems, such as power systems and power electronics [1,21].…”

Section: Introductionmentioning

confidence: 99%

“…> 0, which may lead to considerable conservativeness. Following the work, free weighting matrix and additional nonnegative inequality approaches have been used to improve the conservativeness for the obtained results in [27]. However, many free weighting matrices were introduced, which made the stability result complicated.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Switching Signal Design for Exponential Stability of Uncertain Discrete-Time Switched Time-Delay Systems

Liu

Cai

Zou

2013

Journal of Applied Mathematics

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The switching signal design for exponential stability with ∞ performance of uncertain switched linear discrete-time systems with interval time-varying delay is considered. Systems with norm-bounded parameter uncertainties are considered. By taking a new Lyapunov-Krasovskii (LK) function, sufficient conditions for the existence of a class of stabilizing switching laws are derived in terms of linear matrix inequalities (LMIs) to guarantee the considered switched time-delay system to be exponentially stable. The resulting stability criteria are of fewer matrix variables and are less conservative than some existing ones. In addition, numerical examples are illustrated to show the main improvement.

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“…In this section, we consider some numerical examples in [26,27] to show that the proposed theorem in this paper provides less conservativeness with comparison to some existing results.…”

Section: Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Switching Signal Design for Exponential Stability of Uncertain Discrete-Time Switched Time-Delay Systems

Liu

Cai

Zou

2013

Journal of Applied Mathematics

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“…Consequently, wide efforts have been devoted to address the challenge of switched systems with time varying delays [10,11,13,16,17,19,[22][23][24][25][26]. In addition, from the practical standpoint, it is important to tackle uncertain 2 Mathematical Problems in Engineering switched systems [18,19,23,25,26].…”

Section: Introductionmentioning

confidence: 99%

On Robust Stability Analysis of Uncertain Discrete-Time Switched Nonlinear Systems with Time Varying Delays

Kermani

Sakly

2018

Mathematical Problems in Engineering

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This paper provides new sufficient conditions on robust asymptotic stability for a class of uncertain discrete-time switched nonlinear systems with time varying delays. The main focus will be dedicated to development of new algebraic criteria to break with classical criteria in terms of linear matrix inequalities (LMIs). Firstly, by contracting a new common Lyapunov-Krasovskii functional as well as resorting to the M-matrix proprieties, a novel robust stability criterion under arbitrary switching signals is derived. Secondly, the obtained result is extended for a class of switched nonlinear systems modeled by a set of differences equations by applying the aggregation techniques, the norm vector notion, and the Borne-Gentina criterion. Furthermore, a generalization for switched nonlinear systems with multiple delays is proposed. The main contribution of this work is that the obtained stability conditions are algebraic and simple. In addition, they provide a solution of the most difficult problem in switched systems, which is stability under arbitrary switching, and enable avoiding searching a common Lyapunov function considered as a very difficult task even for some low-order linear switched systems. Finally, two examples are given, with numerical simulations, to show the merit and effectiveness of the proposed approach.

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“…Regarding the stability of switched systems in most of the literatures (Liberzon et al [1999], , Lu et al [2009] and Lien et al [2012], etc), Lyapunov stability theory and its variations or generalizations play a dominant role over an infinite time interval. However, in some practical applications, the system dynamics is mainly considered over a fixed finite time interval, where large values of the state are not acceptable.…”

Section: Introductionmentioning

confidence: 99%

Finite-time Stability Analysis of Switched Linear Singular Systems

Xia

Lian

Shao

et al. 2014

IFAC Proceedings Volumes

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Switching signal design for exponential stability of discrete switched systems with interval time-varying delay

Cited by 15 publications

References 25 publications

Switching Signal Design for Exponential Stability of Uncertain Discrete-Time Switched Time-Delay Systems

Switching Signal Design for Exponential Stability of Uncertain Discrete-Time Switched Time-Delay Systems

On Robust Stability Analysis of Uncertain Discrete-Time Switched Nonlinear Systems with Time Varying Delays

Finite-time Stability Analysis of Switched Linear Singular Systems

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