Finite-Time H ∞ Control for Itô-Type Nonlinear Time-Delay Stochastic Systems

The finite-time H_∞ control problem for an Itô-type stochastic system with nonlinear perturbation and time delay is investigated. First, the finite-time H_∞ control problem for a nonlinear time-delay stochastic system is presented taking into consideration both the transient performance and the capability to attenuate the disturbance of a closed-loop system in a given finite-time interval. Second, using the Lyapunov-Krasoviskii functional method and the matrix inequality technique, some sufficient conditions for the existence of finite-time H_∞ state feedback controller and dynamic-output feedback controller for nonlinear time-delay stochastic systems are obtained. These conditions guarantee the mean-square finite-time bounded-ness of the closed-loop systems and determine the H_∞ control performance index. Third, this problem is transformed into an optimization problem with matrix inequality constraints, and the corresponding algorithms are given to optimize the H performance index and obtain the maximum time-delay. Finally, a numerical example is used to illustrate the effectiveness of the proposed method.

Abstract licence: CC BY-NC-ND

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