Exponential Stability of Switched Systems with Unstable Subsystems: A Mode-Dependent Average Dwell Time Approach

Xie, Dehua; Zhang, Hongyu; Zhang, Hongbin; Wang, Bo

doi:10.1007/s00034-013-9601-8

Cited by 77 publications

(39 citation statements)

References 22 publications

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“…By Lemma 1, it can be concluded that the linear switched system (1) is GUAS for any switching signal satisfying (33) or (34).…”

Section: Lemmamentioning

confidence: 94%

“…By Lemma 2, we can conclude that the filtering error system (5) is GUAS with a mixed weighted H ∞ and passivity performance index γ for any switching signal satisfying (33) or (34). Based on the aforementioned proof, we can conclude that, for any switching signal satisfying (33) or (34), the linear switched system (1) is GUAS and the filtering error system (5) is GUAS with a mixed weighted H ∞ and passivity performance index γ.…”

Section: Lemmamentioning

confidence: 94%

“…The mode-dependent ADT (MDADT) technique was used in the work Xie et al 34 It was shown in the work of Zhao et al 36 that the MDADT can be reduced to the ADT. The mode-dependent ADT (MDADT) technique was used in the work Xie et al 34 It was shown in the work of Zhao et al 36 that the MDADT can be reduced to the ADT.…”

Section: Lemmamentioning

confidence: 99%

“…To guarantee the linear switched system (1) and the filtering error system (5) to be GUAS simultaneously, the switching signal designed in this paper should satisfy (10) and (13) simultaneously. For the case ln μ α < − ln λ η s , (34) can guarantee that the switching signal satisfies (10) and (13) simultaneously. For the case ln μ α < − ln λ η s , (34) can guarantee that the switching signal satisfies (10) and (13) simultaneously.…”

Section: Lemmamentioning

confidence: 99%

“…[33][34][35] However, all the subsystems of switched systems are assumed to be stable. [33][34][35] However, all the subsystems of switched systems are assumed to be stable.…”

Section: Introductionmentioning

confidence: 99%

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Mixed and passive filtering for linear switched systems with average dwell time

Zheng

Guo

Zhang

2017

Adaptive Control & Signal

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In this paper, a new performance index is proposed for switched systems. The new performance index can be viewed as the mixed weighted H ∞ and passivity performance. This new performance index covers the weighted H ∞ performance and the passivity performance as special cases. Based on this new performance index, the weighted H ∞ filtering problem and the passive filtering problem of linear switched systems with unstable subsystems are solved in a unified framework. The states of the filtering error system constructed by the augmentation technique will be divergent when unstable subsystems are activated. To overcome this problem, a set of mode-dependent filters of a Luenberger-like observer type is constructed. The multiple Lyapunov function approach and the average dwell-time technique are employed to solve the mixed filtering problem.New sufficient conditions for the existence of mixed H ∞ and passive filters are developed, which ensure the filtering error system to be asymptotically stable with a prescribed mixed H ∞ and passivity performance index. Moreover, the desired mixed H ∞ and passive filters can be constructed by solving a set of linear matrix inequalities. Finally, numerical examples are given to demonstrate the applicability and advantage of the obtained results. KEYWORDS average dwell time, H ∞ filtering, linear switched systems, passive filtering, unstable subsystemsRecently, the research on switched systems has been developed because of many physical or man-made systems possessing switching features. 1,2 In general, a switched system is composed of a finite number of continuous-time or discrete-time subsystems and a switching signal. The switching signal, which orchestrates the switching among these subsystems, 316

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“…By Lemma 1, it can be concluded that the linear switched system (1) is GUAS for any switching signal satisfying (33) or (34).…”

Section: Lemmamentioning

confidence: 94%

Section: Lemmamentioning

confidence: 94%

Section: Lemmamentioning

confidence: 99%

Section: Lemmamentioning

confidence: 99%

“…[33][34][35] However, all the subsystems of switched systems are assumed to be stable. [33][34][35] However, all the subsystems of switched systems are assumed to be stable.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Mixed and passive filtering for linear switched systems with average dwell time

Zheng

Guo

Zhang

2017

Adaptive Control & Signal

Self Cite

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Pinning and self‐adaptive control to the couple‐group consensus of heterogeneous fractional multi‐agent systems with cooperative‐competitive relation

Cheng

2022

Adaptive Control & Signal

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In this article, the couple-group consensus of a class of heterogeneous fractional multi-agent systems with time-varying delay (HFMASs) has been studied.Based on cooperative-competitive interaction, pinning and self-adaptive controller has been designed to realize the couple-group consensus for this system with single integrator and double integrator fractional-order dynamics. By using Lyapunov function, mode-dependent average dwell time (MDADT) technology, stability theory and delta operator method, some sufficient conditions have been obtained to guard the success of couple-consensus for this HFMASs with fixed or switching topologies. According to these sufficient conditions, the related feasible solutions can be solved by using liner matrix inequality (LMI). In addition, these results are also applicable to the system with weakly connected topology without containing a spanning tree or meeting the demand of equilibrium of degree. Finally, several simulation experiments have been presented to prove the validity of the related results.

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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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Exponential Stability of Switched Systems with Unstable Subsystems: A Mode-Dependent Average Dwell Time Approach

Cited by 77 publications

References 22 publications

Mixed and passive filtering for linear switched systems with average dwell time

Mixed and passive filtering for linear switched systems with average dwell time

Pinning and self‐adaptive control to the couple‐group consensus of heterogeneous fractional multi‐agent systems with cooperative‐competitive relation

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

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