Discrete time robust guaranteed cost control for nonlinear stochastic uncertain systems

This paper presents an approach to discrete time robust nonlinear control based on the use of Sum Quadratic Constraints. The approach involves controllers which include copies of the system nonlinearities in the controller. The nonlinearities being considered are those which satisfy a certain global Lipschitz condition. The linear part of the controller is synthesized using minimax LQG control theory which is closely related to H-infinity control theory and this leads to a nonlinear controller which gives an upper bound on a quadratic cost functional.