H_∞ Control for Stochastic Singular Systems With Time-Varying Delays

Abstract

In this article, we study the H∞ control problems for stochastic singular systems with time-varying delays. Firstly, a new Lyapunov-Krasovskii functional is constructed, employing the free weighting matrix technique and Jensen inequality, the stochastic admissibility criteria in the mean square for stochastic singular time-varying delay systems are proposed on the basis of the auxiliary vector function. Secondly, the state feedback controller is designed such that the resulting closed-loop system meets regular, impulse-free, stochastically stable in the mean square and has H∞ performance γ. In the proof process, the dual equation is used to derive the conditions of stochastic admissibility in the mean square. Finally, a practical example of DC motor model is presented to show the validity of our proposed theoretical results.

Keywords

• Stochastic singular systems
• time-varying delays
• H∞ control
• stochastic admissibility