Delay-dependent robust H ∞ control for uncertain stochastic systems with time-varying delays in state and control input

This note deals with the problems of robust H∞ control for uncertain stochastic systems with a time-varying delay in the state. Based on the Lyapunov stability theory and the stochastic analysis tools, delay-dependent sufficient condition is established in terms of weak coupling linear matrix inequality (LMI) equations. The equations are derived by constructing a more efficient Lyapunov function candidate and combining LMI approach with free-weighting matrix technique. Properties of conservatism are only appeared with free-weighting matrices in a equation, which is coupled with another equation weakly. So the new criteria is of low conservatism with large time-delay, large time-varying rate and small disturbance attenuation. Numerical examples are given to demonstrate the benefits of the proposed criteria.