Stability Analysis and Stabilization of Switched Systems With Average Dwell Time: A Matrix Polynomial Approach

Yuegui Zhou ,Lei Cheng,Hongbin Zhang

doi:10.1109/access.2020.3047261

Yuegui Zhou , Lei Cheng + Show 1 more

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https://doi.org/10.1109/access.2020.3047261

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This paper focuses on stability analysis and stabilization of a switched system under average dwell time criteria in the continuous-time domain. The matrix polynomial approach is applied to the switched system to construct a continuous Lyapunov function and design a more effective controller, which can not only improve the system performance but also lessen the system conservativeness. The stability problem is studied with square matricial representation for the first time. The new method is more applicable than previous work under average dwell time switching with the time-varying controller gains. In addition, new sufficient conditions of stability and stabilization are derived to guarantee the global uniform exponential stability of the switched system. A numerical example is provided to show the advantages of the new method.

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As the basic framework of physical or man-made systems, switched systems have been widely studied in recent decades [1], [2]
MAIN RESULTS the matrix polynomial is used in the Lyapunov function for the stability analysis and stabilization of the switched system
It is noticed that the Lyapunov function degenerates into multiple Lyapunov functions when t − tn = 0

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Introduction

As the basic framework of physical or man-made systems, switched systems have been widely studied in recent decades [1], [2]. The switching signal plays an important role in stability analysis and stabilization of switched systems. Most research results focus on exploiting switching signals to guarantee the global uniform exponential stability of the switched system consisting of various subsystems [11]–[15]. The switching events in control systems could be classified into uncontrolled or controlled [1]. The stability analysis of the switched system with various subsystems under uncontrolled switching is available. The system state and stability will become uncertain. To address this problem, controllers are proposed. For the switched system under controller switching signals, The associate editor coordinating the review of this manuscript and approving it for publication was Guangdeng Zong

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