On Stability of a Class of Switched Nonlinear Systems Subject to Random Disturbances

• Published in: IEEE transactions on circuits and systems. I, Regular papers Vol. 63; no. 12; pp. 2278 - 2289
• Main Authors: Jiao, Ticao, Zheng, Wei Xing, Xu, Shengyuan
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.12.2016; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Asymptotic stability; Average dwell-time; Circuit stability; Disturbances; Dwell time; e^{\lambda t} -weighted (integral) NSS; globally asymptotic stability; Liapunov functions; noise-to-state stability (NSS); Nonlinear systems; probabilistic switching; random switched systems; Stability criteria; Stochastic processes; Switched systems; Switches
• ISSN: 1549-8328; 1558-0806
• DOI: 10.1109/TCSI.2016.2620994

This paper addresses the stability problem for a class of switched nonlinear systems subject to random disturbances whose τ-order moments (τ > 1) are finite. First, some general conditions are given to guarantee the existence and uniqueness of solutions to random switched systems. Next, these results are used to deduce the criteria of noise-to-state stability under probabilistic switching signal. Then, the average dwell-time approach is adopted to study the noise-to-state stability, the e λt -weighted (integral) noise-to-state stability and the global asymptotic stability of random switched systems. All the criteria on global existence and stability of solutions are developed by virtue of multiple Lyapunov functions. Finally, two numerical examples are given to demonstrate the validity of the theoretical results.