Abstract: This paper is based on the stochastic linear quadratic control problem. The
robustness of stabilizability of optimal controller for stochastic multi-time
delay systems with Markovian jumping parameters is investigated. Lyapunov--Krasovskii like functional, stochastic analysis, Ito formula and Schur complement are employed to analyze the exponential stability in mean square for stochastic multi-time delay differential systems with Markovian jumping parameters. The delay dependent and delay independent algebric criteria are established.

Key words: Stochastic Linear quadraic (SLQ) control, Robust stabilization, Delay dependent criteria, Exponential stability in mean square, Markov process