H∞$$ {H}_{\infty } $$ constraint Pareto optimal control for discrete‐time Markov jump linear stochastic systems in finite horizon

Abstract This paper mainly focuses on discrete‐time Markov jump linear stochastic systems (DMJLSSs) with external disturbances and multiplicative noise. Due to the multi‐player in the systems and multi‐objective cost function, the strategy design for these systems is more difficult than the traditional Markov jump stochastic systems. We combine theory with Pareto control and use the weighted sum method of the objective functional of each player to solve the problem of Pareto cooperative game. Four coupled difference matrix‐valued recursion equations (CDMREs) are derived by stochastic bounded real lemma (SBRL). Then, a sufficient and necessary condition for the existence of the Pareto optimal strategy is obtained, and the Pareto solution for every controller is derived under this strategy. A simulation example is given to verify the correctness of the theory.