Finite Horizon H/H Control for Discrete-Time Stochastic Systems With Markovian Jumps and Multiplicative Noise - Ting Hou; Weihai Zhang; Hongji Ma (IEEE transactions on automatic control, 2010)
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.