Stability analysis of switched positive linear systems with stable and unstable subsystems

Zhang, Jishi; Wang, Yan‐Wu; Xiao, Jiang‐Wen; Shen, Yanjun

doi:10.1080/00207721.2013.770938

Cited by 42 publications

(20 citation statements)

References 29 publications

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“…See hypothesis (H1). 6) A similar result is obtained in [24] for switched positive linear systems with both stable and unstable subsystems.…”

Section: 4supporting

confidence: 71%

A Simple Loop Dwell Time Approach for Stability of Switched Systems

Agarwal¹

2018

SIAM J. Appl. Dyn. Syst.

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We introduce a novel concept of simple loop dwell time and use it to give sufficient conditions for stability of a continuous-time linear switched system where switching between subsystems is governed by an underlying graph. We present a slow-fast switching mechanism to ensure stability of the system. We also consider switched systems with both stable and unstable subsystems, and obtain bounds on the dwell time in the stable subsystem and flee time from the unstable subsystem that guarantee the stability of the system.

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“…See hypothesis (H1). 6) A similar result is obtained in [24] for switched positive linear systems with both stable and unstable subsystems.…”

Section: 4supporting

confidence: 71%

A Simple Loop Dwell Time Approach for Stability of Switched Systems

Agarwal¹

2018

SIAM J. Appl. Dyn. Syst.

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“…Positive systems are special systems and they are defined on cones instead of linear spaces. Therefore, some new problems of positive systems appear and they have been studied extensively [3][4][5][6][7][8][9]. For example, controllability and reachability for positive systems have been studied in [10,11].…”

Section: Introductionmentioning

confidence: 99%

l1-Induced State-Feedback Controller Design for Positive Fuzzy Systems

Chen¹,

Shen²

2016

Mathematical Problems in Engineering

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The problem ofl1-induced state-feedback controller design is investigated for positive Takagi-Sugeno (T-S) fuzzy systems with the use of linear Lyapunov function. First, a novel performance characterization is established to guarantee the asymptotic stability of the closed-loop system withl1-induced performance. Then, the sufficient conditions are presented to design the required fuzzy controllers and iterative convex optimization approaches are developed to solve the conditions. Finally, one example is presented to show the effectiveness of the derived theoretical results.

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“…In recent years, many novel results through linear Lyapunov functions have appeared [17]. As is well known, a lot of existing results about positive systems are derived via quadratic Lyapunov functions and many effective methods are available.…”

Section: Introductionmentioning

confidence: 99%

“…The design of state-feedback controllers guaranteeing the closed-loop system to be asymptotically stable has been studied by the linear programming approach in [16]. Moreover, the problem of controller design for positive systems has been investigated by the linear matrix inequality (LMI) approach in [17].…”

Section: Introductionmentioning

confidence: 99%