Stability analysis of 2-D switched systems with multiplicative noise under arbitrary and restricted switching signals

ABSTRACT

This paper introduces a new class of discrete-time two-dimensional (2-D) switched systems with multiplicative noise. Firstly, we extend the definition of the asymptotic stability and establish a sufficient stochastically stability condition for this new model under arbitrary switching signal. Then, by introducing the average dwell time into this new model and combining with the Lyapunov function, we investigate the extended stochastic exponential stability of the 2-D switched systems with multiplicative noise for the restricted switching case. Moreover, some remarks and discussions are given to illustrate the significance of obtained results, which generalise and comprise some previous results the literature. Finally, two examples are provided to show the effectiveness of the theoretical results.

Keywords:

• Multiplicative noise
• average dwell time
• Lyapunov function
• stochastically exponential stability

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was jointly supported by the National Natural Science Foundation of China (61773217, 61374080), the Natural Science Foundation of Jiangsu Province (BK20161552) and Qing Lan Project of Jiangsu Province.