Robust H∞ control for uncertain stochastic markovian time-delay jump system

The problem of robust stochastic stabilization and robust H
_∞
control for a class of uncertain stochastic time-delay Markovian jump system with state and input delays is discussed. Based on Lyapunov-Krasovskii function, a memory-less state feedback controller is designed in order to make the closed-loop system robust stochastic stable and meet H
_∞
performance for all admitted uncertainties. At the same time, a sufficient condition for this problem is given in the form of linear matrix inequalities (LMI). Finally, a numerical example shows the effectiveness of the proposed method.