Guaranteed Cost Control of Stochastic Uncertain Systems with Time-varying Delays

The problem of guaranteed cost robust stable control is considered via state feedback for a class of uncertain stochastic systems with time-varying delay, where the uncertainties are norm bounded. Sufficient conditions for the existence of guaranteed cost controller are given in terms of linear matrix inequalities (LMI). Furthermore, two convex optimization problems with LMI constraints are formulated to design the optimal guaranteed cost controller which minimizes the guaranteed cost of the closed-loop uncertain system with known or unknown initial function. The unknown initial function is assumed to be a white noise process with zero expectation function and unit covariance function. A numerical example is given to illustrate the design method