Stabilization of discrete-time switched positive linear systems via weak switched linear copositive Lyapunov function

Ju, Yanhao; Sun, Yuangong

doi:10.1016/j.automatica.2020.108836

Cited by 37 publications

(11 citation statements)

References 27 publications

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“…Switched system is a hot topic in the academic circles, it is comprised by a complex combination of many subsystems and a switching law. A number of practical systems can be modeled as switched systems, so it deserves further research, for this reason, analyzes of switched systems concerning their stability and performance have been obtained 1‐7 . Meanwhile, networked control systems (NCSs) have also received much research owing to its advantages such as easy operation, high flexibility, maintenance and so on.…”

Section: Introductionmentioning

confidence: 99%

“…A number of practical systems can be modeled as switched systems, so it deserves further research, for this reason, analyzes of switched systems concerning their stability and performance have been obtained. [1][2][3][4][5][6][7] Meanwhile, networked control systems (NCSs) have also received much research owing to its advantages such as easy operation, high flexibility, maintenance and so on. In addition, some challenging problems such as packet dropouts, time-delays have also emerged.…”

Section: Introductionmentioning

confidence: 99%

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Event‐triggered finite‐time guaranteed cost control for networked Takagi‐Sugeno (T‐S) fuzzy switched systems under denial of service attacks

Gao

Zhang

Shi

et al. 2022

Intl J Robust & Nonlinear

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The issue of event-triggered guaranteed cost control (GCC) for networked T-S fuzzy switched systems in the sense of finite-time is addressed in this article. A unified event-based augmented fuzzy switched systems under the denial of service (DoS) attacks is formulated, which leads to the system switching more complex. Using a controller-mode Lyapunov functional approach, sufficient conditions are developed to guarantee the finite-time boundedness (FTB) of the system. Then, a criterion is also proposed to obtain the triggering parameters and controller gains simultaneously. Finally, simulation examples demonstrated the validity of the approach.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Event‐triggered finite‐time guaranteed cost control for networked Takagi‐Sugeno (T‐S) fuzzy switched systems under denial of service attacks

Gao

Zhang

Shi

et al. 2022

Intl J Robust & Nonlinear

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“…Recently, switched positive systems which consist of a series of positive subsystems (modes) and a switching mechanism, have been concerned by many scholars and widely used in different areas, for instance, medical treatment, 2 wireless power control, 3 chemical plants, 4 and so on. To date, many meaningful results on the stability and stabilization of switched positive linear systems (SPLSs) have been reported 5‐10 . As is known, the combination of linear copositive Lyapunov functions and linear programming (LP) technique is a mainstream and powerful method for dealing with the fundamental problems of SPLSs, which differs from quadratic Lyapunov functions incorporated with linear matrix inequalities (LMIs) used in general switched systems.…”

Section: Introductionmentioning

confidence: 99%

“…To date, many meaningful results on the stability and stabilization of switched positive linear systems (SPLSs) have been reported. [5][6][7][8][9][10] As is known, the combination of linear copositive Lyapunov functions and linear programming (LP) technique is a mainstream and powerful method for dealing with the fundamental problems of SPLSs, which differs from quadratic Lyapunov functions incorporated with linear matrix inequalities (LMIs) used in general switched systems.…”

Section: Introductionmentioning

confidence: 99%

L₁ finite‐time control of discrete‐time switched positive linear systems with mode‐dependent persistent dwell‐time switching

Zhang

Chen

2022

Optim Control Appl Methods

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This article mainly investigates the state‐feedback L1$$ {L}_1 $$ finite‐time control problem for discrete‐time switched positive linear systems with mode‐dependent persistent dwell‐time (MDPDT) switching. The MDPDT switching is more general than the common dwell‐time and average dwell‐time switching because it can perfectly model a type of switched systems with hybrid slow and fast switching properties. Considering the positivity of the system, we adopt multiple linear copositive Lyapunov functions instead of traditional quadratic Lyapunov functions and derive sufficient criteria of finite‐time stability by utilizing the linear programming approach. Then the relationship between the lower bound of such switching signals and parameters of the constructed controllers is found successfully, and a sufficient condition to ensure that the closed‐loop switched system maintains positive and L1$$ {L}_1 $$ finite‐time bounded is proposed. Finally, the efficiency of our developed conclusions is validated by two illustrative examples.

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“…A number of methods, such as, common Lyapunov function, 10 multiple Lyapunov functions, 11 switched Lyapunov functions, 12 discretized Lyapunov function, 13 and so on, play important roles in switched systems. Noting that all of the functions mentioned above are quadratic Lyapunov function, which is the most commonly used class of function in the study of switched systems.…”

mentioning

confidence: 99%

Dwell‐time‐based control synthesis of switched positive systems with all unstabilizable subsystems

2022

Intl J Robust & Nonlinear

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This article investigates the robust exponential stabilization of a class of switched positive systems with uncertainties by co-designing controllers for subsystems and dwell time switching strategy. The uncertainties refer to interval uncertainties. One of the distinguishing features is that none of the forced individual subsystems is assumed to be stabilized. The other feature is that the stabilization for the unforced switched system can not be solvable by designing dwell time switching signal. First, for switched positive systems without uncertainties, a type of multiple time-varying co-positive Lyapunov functions is used, and the computable sufficient conditions on the state feedback controller for each subsystem are derived in the framework of dwell time strategy. Moreover, the exponential stabilization problem is solved by confining the lower and upper bounds of the dwell time, restricting the upper bound of derivative of considered Lyapunov function of the active subsystem, and decreasing the Lyapunov function values at successive switching instants of the overall switched system.Then, the results are extended to the robust exponential stabilization case for switched positive systems with uncertainties, and sufficient conditions are given in the same framework of the dwell time for that of the forced switched systems by further designing state feedback controllers. Finally, illustration examples are given to illustrate the effectiveness of the proposed methods.

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Stabilization of discrete-time switched positive linear systems via weak switched linear copositive Lyapunov function

Cited by 37 publications

References 27 publications

Event‐triggered finite‐time guaranteed cost control for networked Takagi‐Sugeno (T‐S) fuzzy switched systems under denial of service attacks

Event‐triggered finite‐time guaranteed cost control for networked Takagi‐Sugeno (T‐S) fuzzy switched systems under denial of service attacks

L₁ finite‐time control of discrete‐time switched positive linear systems with mode‐dependent persistent dwell‐time switching

Dwell‐time‐based control synthesis of switched positive systems with all unstabilizable subsystems

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Stabilization of discrete-time switched positive linear systems via weak switched linear copositive Lyapunov function

Cited by 37 publications

References 27 publications

Event‐triggered finite‐time guaranteed cost control for networked Takagi‐Sugeno (T‐S) fuzzy switched systems under denial of service attacks

Event‐triggered finite‐time guaranteed cost control for networked Takagi‐Sugeno (T‐S) fuzzy switched systems under denial of service attacks

L1 finite‐time control of discrete‐time switched positive linear systems with mode‐dependent persistent dwell‐time switching

Dwell‐time‐based control synthesis of switched positive systems with all unstabilizable subsystems

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L₁ finite‐time control of discrete‐time switched positive linear systems with mode‐dependent persistent dwell‐time switching