Robust H∞ Control for Stochastic Time-Delay Systems with Markovian Jump Parameters via Parameter-Dependent Lyapunov Functionals

This paper deals with the problems of robust stabilization and robust H∞ control for time-delay stochastic systems with Markovian jump parameters and convex polytopic uncertainties. The purpose is the design of state feedback controllers such that the closed-loop system is robustly exponentially stable in the mean square and satisfies a prescribed H∞ performance level. Sufficient conditions for the solvability of the problems are obtained via parameter-dependent Lyapunov functionals. Furthermore, it is shown that desired state feedback controllers can be designed by solving a set of linear matrix inequalities.

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