Stability of switched stochastic nonlinear systems by an improved average dwell time method

Abstract

This paper investigates the stability of switched stochastic continuous-time nonlinear systems in two cases:(1) all subsystems are global asymptotically exponentially stable in the mean (GASiM);(2) both GASiM subsystems and unstable subsystems coexist, and proposes a number of new results on the stability analysis.Firstly, an improved average dwell time (ADT) method is established for the stability of switched stochastic system by extending our previous dwell time method. Especially, an improved mode-dependent average dwell time (MDADT) method for the switched stochastic systems whose subsystems are quadratically stable in the mean is also obtained. Secondly, based on the improved ADT and MDADT methods, several new results on the stability analysis are provided. It should be pointed out that the obtained results have two advantages over the existing results, one is the conditions of the improved ADT method are simplified, the other is that the obtained lower bound of ADT (τ * a ) is also smaller than those obtained by other methods. Finally, two illustrative examples with simulation are given to show the correctness and the effectiveness of the proposed results.Keywords: Switched stochastic nonlinear system, stability in the mean, unstable subsystems, average dwell time, mode-dependent dwell time.2010 MSC: 93D20, 93E15.

H∞ filtering of discrete‐time switched singular systems with time‐varying delays

“…Furthermore, note that is method brings some conservativeness through the use of common parameters for all subsystems. Therefore, to fill the gaps of the ADT method and to solve the problems caused by this approach, a new approach has been developed recently, called mode‐dependent ADT (MDADT), which aims to reduce the conservativeness . It should be noted that the use of one of these two approaches (ADT, MDADT) in the study of the problems of stability, control, and filtering of switched systems, leads to solve some nonlinear conditions to determine the or for each mode.…”

“…Therefore, to fill the gaps of the ADT method and to solve the problems caused by this approach, a new approach has been developed recently, called mode-dependent ADT (MDADT), which aims to reduce the conservativeness. 49,57,58 It should be noted that the use of one of these two approaches (ADT, MDADT) in the study of the problems of stability, control, and filtering of switched systems, leads to solve some nonlinear conditions to determine the * a or * ai for each mode. The stability of switched systems under arbitrary switching is so a desirable importance and also it allows us to consider high control specifications.…”