Finite Horizon $H_{2}/H_{\infty}$ Control for Discrete-Time Stochastic Systems With Markovian Jumps and Multiplicative Noise

In this note, we consider the finite horizon mixed
H

₂
/
H

_∞
control problem for discrete-time stochastic linear systems subject to Markov jump parameters and multiplicative noise. Firstly, we derive a stochastic bounded real lemma (SBRL), which is used to establish a necessary and sufficient condition for the existence of the mixed
H

₂
/
H

_∞
control via the solvability of four coupled difference matrix-valued recursions (CDMRs). Moreover, a state feedback
H

₂
/
H

_∞
controller is designed by means of the solutions of CDMRs.