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Stabilization of two dimensional switched systems with unstable modes based on the weighted average dwell time
Qiang Yu1,2, Wangxian Su3,4, Yanping Guo3,4
1Shanxi Key Laboratory of Cryptography and Data Security, Shanxi Normal University, Taiyuan, 030031, China. yuqiang111111@126.com.
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This study focuses on the stabilization of two-dimensional (2-D) switched systems utilizing the Fornasini-Marchesini local state-space model. Without any controller, by designing a set of switching signals subject to weighted average dwell time approach, the 2-D switched systems with all subsystems unstable could be stabilized. The weighted average dwell time approach used in this paper is more effective than mode-dependent dwell time and average dwell time used in other literature. Furthermore, the introduction of a quasi-time-dependent Lyapunov functional ensures the asymptotically stability of the 2-D switched system. This paper addresses the stabilization challenges of 2-D switched systems by employing Fornasini-Marchesini local state-space model, offering a comprehensive approach to a field that is critical to both academic and industrial domains. The efficacy of these methodologies are demonstrated through an illustrative example.
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