Minimax Control of Markov Jump Linear Systems⋆

This paper introduces and focuses on a new control strategy for continuous-time Markov jump linear systems denominated minimax control. It generalizes switching and linear parameter varying control strategies and is determined such as to preserve stochastic stability and guaranteed H2 performance. The special classes of Markov mode dependent and mode independent con-trol are considered. The design methodology is characterized by minimax problems for which the existence of a saddle point is the central issue to be taken into account. As a natural application, Markov jump linear systems state feedback control design is dis-cussed under this framework. A numerical example illustrates the theoretical results