Stability Analysis of a Class of Switched Nonlinear Systems with an Improved Average Dwell Time Method

Abstract

This paper investigates the stability of switched nonlinear (SN) systems in two cases: (1) all subsystems are globally asymptotically stable (GAS), and (2) both GAS subsystems and unstable subsystems coexist, and it proposes a number of new results on the stability analysis. Firstly, an improved average dwell time (ADT) method is presented for the stability of such switched system by extending our previous dwell time method. In particular, an improved mode-dependent average dwell time (MDADT) method for the switched systems whose subsystems are quadratically stable (QS) is also obtained. Secondly, based on the improved ADT and MDADT methods, several new results to the stability analysis are obtained. It should be pointed out that the obtained results have two advantages over the existing ones; one is that the improved ADT method simplifies the conditions of the existing ADT method, the other is that the obtained lower bound of ADT (${\tau }_a^{*}$) is also smaller than that obtained by other methods. Finally, illustrative examples are given to show the correctness and the effectiveness of the proposed methods.