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

Volume 18, Issue 1, pp 37--48 Publication Date: December 31, 2017       Article History
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### Authors

Rongwei Guo - School of Science, Qilu University of Technology, Jinan 250353, P. R. China Yuangong Sun - School of Mathematical Sciences, University of Jinan, Jinan 250022, P. R. China Ping Zhao - School of Electrical Engineering, University of Jinan, Jinan 250022, P. R. China

### 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 $(\tau_a^*)$ 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

•  93D20
•  93E15

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