Infinite horizon H2/H∞H2/H∞ control for stochastic systems with Markovian jumps

This paper studies robust H2/H∞H2/H∞ control problem for systems subjected to multiplicative noise and Markovian parameter jumps. A necessary/sufficient condition for the existence of H2/H∞H2/H∞ control is presented by means of two coupled algebraic Riccati equations, respectively. Finally, a suboptimal H2/H∞H2/H∞ controller design algorithm is also obtained by solving a convex optimization problem.