Asynchronously switching control of discrete-time switched systems with a $ \Phi $-dependent integrated dwell time approach

Qiang Yu; Na Xue; Qiang Yu; Na Xue

doi:10.3934/math.20231501

AIMS Mathematics

2023, Volume 8, Issue 12: 29332-29351. doi: 10.3934/math.20231501

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Asynchronously switching control of discrete-time switched systems with a $ \Phi $-dependent integrated dwell time approach

Qiang Yu ^,,
Na Xue

School of Mathematics and Computer Science, Shanxi Normal University, Taiyuan 030032, China

Received: 12 September 2023 Revised: 12 October 2023 Accepted: 15 October 2023 Published: 30 October 2023
MSC : 34D20, 93D15

In this paper, the asynchronous control problem is investigated and a multiple convex Lyapunov functions (MCLF) approach is introduced for a class of discrete-time switched linear systems under the $ \Phi $-dependent integrated dwell time ($ \Phi $DIDT) switching strategy. For the problem of asynchronous switching, this paper considers that Lyapunov functions may jump when the subsystem switches or the controller changes. Thus, the constructed MCLF is dependent on both the asynchronous interval and the synchronous interval, and the synchronous interval is divided into the convex interval and non-convex interval parts. Some sufficient conditions of stability with Linear matrix inequality (LMI) forms are obtained, and the asynchronous controller is designed to guarantee the globally uniform exponential stability of the system under study. In addition, the proposed method can degenerate to the existing methods to deal with the asynchronous control problem. Finally, a numerical example illustrates the superiority of the proposed method.
Citation: Qiang Yu, Na Xue. Asynchronously switching control of discrete-time switched systems with a $ \Phi $-dependent integrated dwell time approach[J]. AIMS Mathematics, 2023, 8(12): 29332-29351. doi: 10.3934/math.20231501

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Abstract

In this paper, the asynchronous control problem is investigated and a multiple convex Lyapunov functions (MCLF) approach is introduced for a class of discrete-time switched linear systems under the $ \Phi $-dependent integrated dwell time ($ \Phi $DIDT) switching strategy. For the problem of asynchronous switching, this paper considers that Lyapunov functions may jump when the subsystem switches or the controller changes. Thus, the constructed MCLF is dependent on both the asynchronous interval and the synchronous interval, and the synchronous interval is divided into the convex interval and non-convex interval parts. Some sufficient conditions of stability with Linear matrix inequality (LMI) forms are obtained, and the asynchronous controller is designed to guarantee the globally uniform exponential stability of the system under study. In addition, the proposed method can degenerate to the existing methods to deal with the asynchronous control problem. Finally, a numerical example illustrates the superiority of the proposed method.

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