New finite-time stability conditions of linear switched singular systems with finite-time unstable subsystems

Wei, Jumei; Zhang, Xiuxiu; Zhi, Huimin; Mu, Xiaomin; Zhu, Xun-Lin

doi:10.1080/03081079.2019.1615907

Cited by 10 publications

(14 citation statements)

References 29 publications

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“…In Theorem 3.2, as in Wei, Zhang, et al (2019), we design slow and fast switching for stable subsystems and unstable subsystems, respectively, in our switching scheme. It not only gives the lower bounds that stable subsystems should dwell on but also provides the upper bounds for unstable subsystems.…”

Section: Remark 33mentioning

confidence: 99%

“…Consequently, the MDADT switching law is more suitable in practice than the ADT switching law (J. Liu et al, 2015;Wei, Zhang, et al, 2019;Wei et al, 2020;Zhao et al, 2011). Furthermore, the MDADT switching law consists of a slow mode-dependent average dwell time (SMDADT) switching and a fast mode-dependent average dwell time (FMDADT) switching.…”

Section: Introductionmentioning

confidence: 99%

“…For switched singular systems without delay, finite-time stabilization for the system under the ADT approach was studied in Wang et al (2015). The FTS problem for the system with finite-time unstable subsystems based on the MDADT technique was studied in Wei, Zhang, et al (2019) for the continuous-time case and in Wei et al (2020) for the discrete-time case. Moreover, the E-exponential stability problem for the system with stable and unstable subsystems by employing the MDADT switching law was investigated in .…”

Section: Introductionmentioning

confidence: 99%

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Finite-time stability and boundedness for linear switched singular positive time-delay systems with finite-time unstable subsystems

Yimnet

Niamsup

2020

Systems Science & Control Engineering

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In this paper, the problem of finite-time stability and finite-time boundedness for a class of linear switched singular positive time-delay systems with finite-time unstable subsystems is investigated. Necessary and sufficient positivity conditions for the systems are firstly presented by using the state-space singular value decomposition and monomial coordinate transformation methods. A class of quasi-alternative switching signals is then designed to analyze the switching behaviours of the systems. Mode-dependent average dwell time (MDADT) switching, consisting of a slow modedependent average dwell time (SMDADT) switching and a fast mode-dependent average dwell time (FMDADT) switching, is applied to the systems whose subsystems are stable and unstable. By establishing a suitable copositive Lyapunov-Krasovskii functional and adopting the MDADT switching strategy, all sufficient conditions guaranteeing the finite-time stability and finite-time boundedness of the considered systems are formulated in terms of linear vector inequalities as well as linear matrix inequalities. Several numerical examples are provided to illustrate the effectiveness of the proposed methods. Notably, a positive electrical circuit model is utilized to demonstrate the applicability of the theoretical results.

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Section: Remark 33mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Finite-time stability and boundedness for linear switched singular positive time-delay systems with finite-time unstable subsystems

Yimnet

Niamsup

2020

Systems Science & Control Engineering

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“…In the LMI and DLMI frameworks, the finite‐time control has been combined with many other specific systems or problems and obtained significant results, including FTS control of discrete‐time systems, 12 time‐delayed systems, 13 switched systems, 14 networked control systems, 15‐17 and FTS‐based robust control 18 . For example, Li et al developed a Lyapunov–Razumikhin functional to establish some less‐conservative FTS conditions for time‐delay systems; 19 Wei et al addressed the FTS problem of linear switched singular systems with finite‐time unstable subsystems, and sufficient FTS conditions are obtained by using dynamic decomposition technique and average dwell time method 20 . Although the research on FTS has covered plenty of control fields and made substantial progress, the study of FTS on large‐scale systems is hardly seen in the literature.…”

Section: Introductionmentioning

confidence: 99%

Decentralized finite‐time control for a class of large‐scale systems with symmetrically interconnected subsystems

Sun

Tang²

2022

Adv Control Appl

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The finite-time stability (FTS) of a symmetrically interconnected system is studied under the consideration of utilizing the system structural properties to reduce the complexity of analysis. The FTS of this kind of large-scale system can be guaranteed by that of two lower dimensional systems. The concept of mixed stability, taking care of both transient and steady-state performances of a system, is introduced. Based on the FTS analysis, a decentralized finite-time controller via state feedback is given to stabilize the large-scale system. Meanwhile, an observer-based decentralized output feedback controller is provided to make the closed-loop system finite-time stable. The FTS conditions and related decentralized stabilization controller parameters are both derived from solving some differential or algebraic linear matrix inequalities.

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“…As well as the FTS and the stabilization for the system were respectively studied in [10] and [9]. Recently, the FTS problem for the system with finite-time unstable subsystems was investigated in [29]. Some valuable results have been reported in [17,24] for singular switched systems with time-delay.…”

Section: Introductionmentioning

confidence: 99%

Finite-Time Stability of Discrete Linear Singular Switched Positive Systems with Time-Delay by a Mode-Dependent Average Dwell Time Approach

Yimnet¹,

Niamsup²

2020

DSA

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The problem of positivity and finite-time stability for a class of discrete linear singular switched time-delay systems with mode-dependent average dwell time (MDADT) approach is investigated in this paper. New necessary and sufficient conditions for the positivity of the system are presented by employing the state-space singular value decomposition and monomial coordinate transformation methods. By establishing a novel copositive Lyapunov function and applying the MDADT switching strategy, some computable sufficient conditions are formulated to ensure the finite-time stability for a class of discrete linear singular switched positive time-delay systems in terms of algebraic linear matrix inequalities. Two numerical experiments are provided to illustrate the effectiveness and less conservativeness of the proposed results.

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New finite-time stability conditions of linear switched singular systems with finite-time unstable subsystems

Cited by 10 publications

References 29 publications

Finite-time stability and boundedness for linear switched singular positive time-delay systems with finite-time unstable subsystems

Finite-time stability and boundedness for linear switched singular positive time-delay systems with finite-time unstable subsystems

Decentralized finite‐time control for a class of large‐scale systems with symmetrically interconnected subsystems

Finite-Time Stability of Discrete Linear Singular Switched Positive Systems with Time-Delay by a Mode-Dependent Average Dwell Time Approach

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