Quantitative measures of robustness for LQG optimal control systems including delayed perturbations

Linear quadratic Gaussian (LQG) optimal control systems subject to delayed time-varying and nonlinear perturbations are considered. Some robust stability conditions are derived which result in some bounds on the delayed perturbations so that the systems can remain stable in the sense of uniform ultimate boundedness. The modified Lyapunov equation and the improved Razumikhin-type theory are employed to investigate such robust stability conditions for such a class of LQG optimal control systems. Finally, a numerical example is given to demonstrate the validity of the results.