A unified framework of convex stability conditions for 2-D switched systems with stable or unstable modes

Shang, Xinxin; Yu, Xinghu; Gao, Huijun; Shi, Yang

doi:10.1016/j.automatica.2022.110264

Cited by 5 publications

(3 citation statements)

References 41 publications

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“…And these two models are inherently identical and can be interconverted by appropriate alternative techniques, and many partial differential equations (PDEs) in practical backgrounds can be transformed into these model descriptions through suitable state transitions (Du et al, 2001). To date, some important issues such as stability, control, and filtering of 2D systems have been extensively studied and yielded fruitful results (Ahn et al, 2015;Malik et al, 2022;Zhuang et al, 2022). Recently, 2D MJSs with asynchronous modes have attracted the attention of many researchers and some preliminary results have been reported (Shen et al, 2019b(Shen et al, , 2022Tao et al, 2022a).…”

Section: Introductionmentioning

confidence: 99%

Asynchronous event-triggered guaranteed cost control of two-dimensional Markov jump Roesser systems

Liu

Yang

Zhu

et al. 2023

Transactions of the Institute of Measurement and Control

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This paper deals with the problem of asynchronous event-triggered guaranteed cost control for two-dimensional Markov jump systems in Roesser model. The hidden Markov model is introduced to characterize the asynchronous phenomenon induced by imperfect mode detection, and a hidden Markov model-based event-triggered mechanism is employed in controller design to reduce the communication burden of the network. By using the quadratic Lyapunov function technique, some sufficient criteria are developed to ensure the asymptotic stability of the addressed system with a guaranteed cost value under three different boundary conditions. Finally, an optimization algorithm with linear matrix inequality constraints is formulated to design the optimal asynchronous event-triggered guaranteed cost control law, and a simulation example is considered to illustrate its validity.

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Section: Introductionmentioning

confidence: 99%

Asynchronous event-triggered guaranteed cost control of two-dimensional Markov jump Roesser systems

Liu

Yang

Zhu

et al. 2023

Transactions of the Institute of Measurement and Control

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“…However, the previous literature focused on the stability of switched systems with only stable modes or unstable modes. As far as we know, few results have been obtained regarding the stability of switched systems with both stable and unstable modes [ 26 , 27 ]. By introducing a unit switching sequence and sequence generator, a unified stability framework for two-dimensional discrete-time switched systems was established in [ 26 ].…”

Section: Introductionmentioning

confidence: 99%

“…As far as we know, few results have been obtained regarding the stability of switched systems with both stable and unstable modes [ 26 , 27 ]. By introducing a unit switching sequence and sequence generator, a unified stability framework for two-dimensional discrete-time switched systems was established in [ 26 ]. The exponential stability of switched positive systems with both stable and unstable modes was discussed through a multiple piecewise continuous linear copositive Lyapunov function method in [ 27 ].…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis of Switched Linear Singular Systems with Unstable and Stable Modes

Xiong,

Wang,

Huo

et al. 2023

Entropy

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In this paper, stability is studied for a class of switched singular systems containing both stable and unstable modes. By introducing a time-varying piecewise Lyapunov function (TVPLF) and a mode-dependent average dwell time (ADT) switching rule, the computable sufficient conditions for system stability are derived. The time-varying piecewise Lyapunov functions are piecewise continuously differentiable on every mode (but may not be differentiable at the interpolating points of the dwell time). This Lyapunov function method is particularly advantageous in overcoming the limitations of traditional multiple Lyapunov function (MLF) methods, which may not have a feasible solution when dealing with switched systems containing only unstable modes. As such, the TVPLF offers greater flexibility in application. Compared with the conventional ADT switching rule, the mode-dependent ADT switching rule not only enables each mode to have its own ADT but also allows for its own switching strategy. Specifically, the stable mode adopts a slow switching strategy while the unstable mode adopts a fast one, thereby reducing the conservatism of the ADT switching rule. Furthermore, based on the stability analysis, the time-varying controllers are proposed to stabilize the switched singular system, which can be expressed as the sequential linear combination of a series of linear state feedback on each mode. The proposed controllers are continuous for each mode, which are different from the controllers designed through the traditional MLF and MDLF methods, where the controllers designed by traditional MLF are the time-invariant linear state feedback in each mode while the controllers designed by the MDLF are piecewise continuous for each mode.

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PID Output-Feedback Control and Filtering for Positive Roesser System

Zhang,

Liang,

2023

Circuits Syst Signal Process

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A unified framework of convex stability conditions for 2-D switched systems with stable or unstable modes

Cited by 5 publications

References 41 publications

Asynchronous event-triggered guaranteed cost control of two-dimensional Markov jump Roesser systems

Asynchronous event-triggered guaranteed cost control of two-dimensional Markov jump Roesser systems

Stability Analysis of Switched Linear Singular Systems with Unstable and Stable Modes

PID Output-Feedback Control and Filtering for Positive Roesser System

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