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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 H∞$$ {H}_{\infty } $$ 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. [ABSTRACT FROM AUTHOR]

This paper considers quadratic stabilizability and H ∞ feedback control for stochastic discrete-time uncertain systems with state- and control-dependent noise. Specifically, the uncertain parameters considered are norm-bounded and external disturbance is an l2-square summable stochastic process. Firstly, both quadratic stability and quadratic stabilization criteria are presented in the form of linear matrix inequalities (LMIs). Then we design the robust H ∞ state and output feedback H ∞ controllers such that the system with admissible uncertainties is not only quadratically internally stable but also robust H ∞ controllable. Sufficient conditions for the existence of the desired robust H ∞ controllers are obtained via LMIs. Finally, some examples are supplied to illustrate the effectiveness of our results. [ABSTRACT FROM AUTHOR]