Infinite horizon control for discrete-time time-varying Markov jump systems with multiplicative noise

In this paper we consider the infinite horizon H 2 / H ∞ control problem for discrete-time time-varying linear systems subject to Markov jump parameters and state-multiplicative noise. A stochastic version of a bounded real lemma is firstly developed for a general class of discrete-time time-varying Markov jump systems with state- and disturbance-multiplicative noise. By which we present a necessary and sufficient condition for the solvability of the H 2 / H ∞ control problem in terms of four coupled discrete-time Riccati equations. Moreover, the obtained design is applied to a macroeconomic problem to verify its effectiveness.