Average dwell time approach to finite-time stabilization of switched singular linear systems

Wang, Yijing; Zou, Yanchao; Liu, Yuhua; Shi, Xiaomeng; Zuo, Zhiqiang

doi:10.1016/j.jfranklin.2015.05.022

Cited by 38 publications

(25 citation statements)

References 26 publications

(21 reference statements)

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“…. In this paper, Caputo fractional-order operator is used, where definition of the left Caputo fractional-order derivatives is given [14,15] as follows:…”

Section: Preliminariesmentioning

confidence: 99%

“…During the past years, singular systems also known as differential-algebraic systems, semistate systems, descriptor systems, or generalized state-space systems have attracted considerable attention because of their significant applications in diverse areas [13][14][15][16]. Practically, many physical systems can be better described by singular systems than by regular systems.…”

Section: Introductionmentioning

confidence: 99%

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Closed-loop iterative learning control for fractional-order linear singular time-delay system: PDα-type

Lazarević¹,

Cvetković²,

Mandić³

2018

Sci Tech Rev

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In this paper a closed-loop PD α-type iterative learning control (ILC) of fractional order linear singular time-delay system is considered. The sufficient conditions for the convergence in time domain of the proposed PD-alpha type ILC for a class of fractional order singular system are given by the corresponding theorem together with its proof. Also, for the first time, we proposed a proposed ILC PD α type for a given class of uncertain, fractional order, singular systems. Finally, the validity of the proposed PD α ILC scheme for a class of fractional order singular time-delay system is verified by a numerical example.

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“…. In this paper, Caputo fractional-order operator is used, where definition of the left Caputo fractional-order derivatives is given [14,15] as follows:…”

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Closed-loop iterative learning control for fractional-order linear singular time-delay system: PDα-type

Lazarević¹,

Cvetković²,

Mandić³

2018

Sci Tech Rev

View full text Add to dashboard Cite

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“…There are many models, such as economics systems, complex network systems, and so on, that can be described as switched singular systems. Previous research studies, including those on stability analysis, finite‐time stabilization, L 1 ‐gain and l ∞ ‐gain analysis, H ∞ control problems, observer design for switched systems, and Markov jump systems, had a lot of excellent results . In practice, since the state variables are always unmeasurable, the observer‐based control for switched singular systems is more important and useful for practical systems.…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, in many practical systems, the state variable should be less than a certain bound during a fixed time interval, such as asynchronous transfer mode network control and aircraft control; hence, finite‐time stability is useful in these cases . In recent years, finite‐time stability and stabilization and H ∞ finite‐time control problems have been widely investigated . For example, Lin et al discussed finite‐time boundedness and L 2 ‐gain analysis for switched delay systems and switched systems with ADT, respectively.…”

Section: Introductionmentioning

confidence: 99%

“…For nonlinear switched systems, finite‐time stabilization of switched nonlinear systems with partial unstable modes was of concern in the work of Wang et al, and H ∞ finite‐time control for discrete‐time switched nonlinear systems was discussed in the works of Xiang and Xiao . Finite‐time control and finite‐time filtering were discussed in the works of Ren et al Wang et al considered finite‐time stability and stabilization for switched singular linear systems with the ADT approach. Wang et al discussed finite‐time stabilization for Lipschitz nonlinear discrete‐time singular Markov jump systems with the ADT approach, and sufficient LMI conditions were obtained.…”

Section: Introductionmentioning

confidence: 99%

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Observer‐based finite‐time stabilization for discrete‐time switched singular systems with quadratically inner‐bounded nonlinearities

Sun

2019

Intl J Robust & Nonlinear

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Summary This paper discusses the observer‐based finite‐time stabilization for discrete‐time switched singular systems with quadratically inner‐bounded nonlinear terms. Firstly, based on the Luenberger‐like observer, by using the average dwell time approach, sufficient conditions are proposed to make closed‐loop systems be regular, be causal, as having a unique solution, and be uniformly finite‐time bounded. Then, a new linear matrix inequality sufficient condition for the existence of an observer‐based controller is obtained by using certain matrix decoupling techniques, and the controller is designed. In this paper, the conditions proposed not only give the observer‐based controller design methods but also guarantee the existence and uniqueness of solution for the systems. Since the quadratically inner‐bounded nonlinearities are more general than Lipschitz nonlinearities and one‐sided Lipschitz nonlinearities, compared with previous works, the proposed controller design methods in this paper are also more general than the existing ones. Finally, numerical examples are provided to illustrate the effectiveness of the methods proposed in this paper.

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Stability of highly nonlinear neutral stochastic delay system with both stable and unstable subsystems

Lin,

Shi,

Wang

2024

Intl J Robust & Nonlinear

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The article addresses the exponentially stable conditions of the highly nonlinear neutral stochastic delayed system (HNNSDS) that contains unstable subsystems apart from stable ones under Markov switching. By the application of the mode‐dependent average dwell time (MDADT) as well as Lyapunov function approach, the general switching condition still satisfies even when the partial Lyapunov coefficients are negative. In addition, the degree of instability is combined with the study of switching signals. On this basis, the case when the system contains only stable subsystems is also investigated. A well‐known switching condition is obtained, establish the foundation of the comparison with more complex cases involving unstable subsystems. The simulation processes are eventually provided to verify rationality of the obtained criteria.

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Average dwell time approach to finite-time stabilization of switched singular linear systems

Cited by 38 publications

References 26 publications

Closed-loop iterative learning control for fractional-order linear singular time-delay system: PDα-type

Closed-loop iterative learning control for fractional-order linear singular time-delay system: PDα-type

Observer‐based finite‐time stabilization for discrete‐time switched singular systems with quadratically inner‐bounded nonlinearities

Stability of highly nonlinear neutral stochastic delay system with both stable and unstable subsystems

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