SUFFICIENT CONDITIONS FOR ROBUST STABILITY OF LQG OPTIMAL-CONTROL SYSTEMS INCLUDING DELAYED PERTURBATIONS

Linear-quadratic Gaussian (LQG) optimal control systems subject to tim e-varying delay and nonlinear state perturbations are considered. Some robust stability conditions are derived which result in several bound s on the delayed state perturbations so that the uncertain linear-quad ratic Gaussian optimal control systems with time-varying delay can rem ain stable in the sense of uniform ultimate boundedness. The modified Lyapunov equation and the improved Razumikhin-type theorem are employe d to investigate such robust stability conditions. Finally, a numerica l example is given to demonstrate the validity of the results.