ABSTRACT

This chapter extends the H2/H control theory developed in other chapters to linear Markov jump systems. The linear discrete-time H2/H; control with Markov switching and multiplicative noise is studied for finite and infinite horizon cases. The chapter also considers the H2/H8 control of linear Ito-type differential systems with Markov jump. It then discusses the relationship between the solvability of H2/H control and the existence of a Nash equilibrium strategy. As one of the most basic dynamics models, Markov jump linear systems can be used to represent random failure processes in the manufacturing industry and some investment portfolio models, and have been researched extensively in the monographs. Stability analysis of Markovian jumping systems was dealt with in and robust H control can be found for systems with multiplicative noise.