Abstract
The paper investigates mean-square exponential stabilization for a class of nonlinear switched stochastic systems with interval time-varying delay under asynchronous switching. Specifically, the delay occurs not only in the state equation, but also in the switching signal from the controller, which brings the difficulty of controller design to achieve mean-square exponential stabilization. Based on the Lyapunov stability theory, a new piecewise multi-Lyapunov–Krasovskii functional dependent on the size of time delay is constructed. By utilizing the matrix inequality technique and the average dwell time approach, delay-dependent sufficient conditions are given to guarantee mean-square exponential stabilization for nonlinear switched stochastic systems under asynchronous switching. In accordance with the method, we also design state feedback controllers of the switched stochastic systems under asynchronous switching through special operations of matrices and Schur complement. Finally, a numerical example and a practical example of river pollution control are provided to show the effectiveness of the approach proposed in this paper.
Highlights
During the last two decades, hybrid systems have become increasingly important in contemporary society both in science and technology due mainly to the fact that hybrid systems have been extensively applied in many fields such as pattern recognition [1], network control [2], power systems [3], automotive systems [4], communication systems [5], neural networks [6], and so on
Robust guaranteed cost control for a class of uncertain neutral system with time-varying delays was investigated in [23], delay-dependent and delay-independent criteria were proposed for the stabilization of considered systems, state feedback control was considered to stabilize the uncertain neutral system, and upper bounds on the closed-loop cost function were given. [24] obtained sufficient conditions with delay-dependent guaranteeing the exponential stability by a common Lyapunov functional (CLF)
The important information of hm and hM is taken into full consideration, which may overcome the conservatism of quadratic mean-square exponential stability conditions for nonlinear switched stochastic systems with interval time-varying delay under asynchronous switching
Summary
During the last two decades, hybrid systems have become increasingly important in contemporary society both in science and technology due mainly to the fact that hybrid systems have been extensively applied in many fields such as pattern recognition [1], network control [2], power systems [3], automotive systems [4], communication systems [5], neural networks [6], and so on. By following this idea, [22] studied the delay-dependent stability analysis and relevant control problems for nonlinear switched with interval time-varying delay based on Lyapunov–Krasovskii functional method. . In addition, by constructing the parameter-dependent Lyapunov– Krasovskii functional and the average dwell time approach, the exponential stabilization problem for a class of nonlinear switched systems with mixed delays under asynchronous switching was investigated in [32].
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