Abstract
This paper addresses stabilization problem for a class of switched stochastic systems with time delays by using piecewise Lyapunov–Krasovskii functional method. Asynchronous switching means the switching of the controller has a time delay to the switching of the system. We provide a set of Lyapunov–Krasovskii-type sufficient conditions for establishing the mean-square exponential stability. The mean-square exponential stability condition for the resulting closed-loop system is firstly derived by further allowing the Lyapunov–Krasovskii functional to increase during the running time of the active subsystem with the mismatched controller. Then, the corresponding solvability condition for stabilizing controllers is established. Finally, we present an example to show the effectiveness of the developed theory.
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This work was supported in part by the NSFC under Grants 61174058 and 61004020, and the Program for New Century Excellent Talents in University NCET-09-0257.
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Wang, YE., Sun, XM. & Zhao, J. Stabilization of a Class of Switched Stochastic Systems with Time Delays Under Asynchronous Switching. Circuits Syst Signal Process 32, 347–360 (2013). https://doi.org/10.1007/s00034-012-9439-5
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DOI: https://doi.org/10.1007/s00034-012-9439-5