Delay-dependent stabilization for delay stochastic differential systems with Markov jumping parameters based on SLQ controllers

Abstract

This paper is based on the stochastic linear quadratic (SLQ) control problem. The robustness of stabilizability of optimal controller for time-delay stochastic differential systems with Markov jumping parameters is investigated. Stochastic Lyapunov-Krasovskii functional, stochastic analysis, Ito formula, Schur complement and slack matrices are employed to analyze the exponential stability in mean square for stochastic delay differential systems with Markov jumping parameters. The delay-dependent algebraic criteria are given in linear matrix inequalities (LMIs).