ROBUST EXPONENTIAL STABILITY OF SWITCHED DELAY INTERCONNECTED SYSTEMS UNDER ARBITRARY SWITCHING

Abstract

Abstract: The problem of robust exponential stability for a class of switched nonlinear dynamical systems with uncertainties and unbounded delay is addressed. On the assumption that the interconnected functions of the studied systems satisfy the Lipschitz condition, by resorting to vector Lyapunov approach and M-matrix theory, the sufficient conditions to ensure the robust exponential stability of the switched interconnected systems under arbitrary switching are obtained. The proposed method, which neither require the individual subsystems to share a Common Lyapunov Function (CLF), nor need to involve the values of individual Lyapunov functions at each switching time, provide a new way of thinking to study the stability of arbitrary switching. In addition, the proposed criteria are explicit, and it is convenient for practical applications. Finally, two numerical examples are given to illustrate the correctness and effectiveness of the proposed theories.

Key words: interconnected systems, robust stability, switching rule, unbounded delay

Huanbin XUE, Jiye ZHANG. ROBUST EXPONENTIAL STABILITY OF SWITCHED DELAY INTERCONNECTED SYSTEMS UNDER ARBITRARY SWITCHING[J].Acta mathematica scientia,Series B, 2018, 38(6): 1921-1938.

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