Robust H2/H∞ control for discrete-time stochastic systems with Markovian jumps and multiplicative noise: Finite horizon case

In this paper, we consider the finite horizon H
2
/H
∞
control problem for discrete-time stochastic linear systems subject to Markov jump parameters and multiplicative noise. A necessary and sufficient condition is established for the existence of the mixed H
2
/H
∞
control via the solvability of four coupled difference matrix-valued equations(CDMEs). Moreover, the state feedback controller is designed by means of the solutions of CDMEs.