Finite horizon H2/H∞ control of time-varying stochastic systems with Markov jumps and (x, u, v)-dependent noise

This study investigates the finite horizon H₂/H_∞ control of time-varying stochastic Markov jump systems (SMJSs) with state, control and disturbance-dependent noise. Firstly, the stochastic bounded real lemma of SMJSs is established, which by itself has theoretical importance. Secondly, several necessary and sufficient conditions for H₂/H_∞ control of SMJSs are proposed by means of coupled generalised differential Riccati equations. Finally, two numerical examples are given to show the effectiveness of the obtained results.