Design of minimax robust LQG controllers under parameter and noise uncertainties

The problem of design of minimax robust LQG controllers for linear systems with parameter and noise uncertainties is considered in this paper. Necessary and sufficient conditions for converting this problem to a two‐person, zero‐sum continuous game problem are presented. A simple procedure for design of a suboptimal minimax robust LQG controller, i.e., the LQG controller for least‐favourable model, is proposed. Necessary and sufficient conditions for the existence of a saddle point are established. Under these conditions, the controller obtained is exactly the minimax LQG controller. When there does not exist a saddle point, the worst‐case error between the controller obtained and the minimax robust LQG controllers under described uncertainties is bounded.