Stability analysis of time-varying switched systems via indefinite difference Lyapunov functions. (May 2023) - Li, Huijuan
Abstract: Asymptotic stability of time-varying switched systems is investigated in this paper. The less conservative sufficient criteria for asymptotic stability of time-varying discrete-time switched systems are proposed via common indefinite difference Lyapunov functions and multiple indefinite difference Lyapunov functions introduced in this note, respectively. Common indefinite difference Lyapunov functions can be used to analyze stability of a switched system with asymptotic stable subsystems and arbitrary switching signal. Multiple indefinite difference Lyapunov functions can be used to investigate stability of a switched system with unstable subsystems and a given switching signal. The difference of the proposed Lyapunov function may be positive at some instants for an asymptotically stable subsystem. We compare these main results and illustrate the effectiveness of the obtained theorems by three numerical examples. Highlights: The concept of CIDLF for a time-varying switched discrete-time system is introduced. Sufficient criteria for asymptotic stability of systems are proposed via CIDLFs. The concept of MIDLF for a time-varying switched discrete-time system is proposed. Sufficient criteria for asymptotic stability of systems are proposed via MIDLFs. The comparison between the main results is discussed.