In this article, the [Formula: see text] control problem of a class of singular Markov jump systems with time-varying inputs and state delays is investigated. Based on the Lyapunov stability theory, by constructing a different Lyapunov–Krasovskii functional, the sufficient conditions of being stochastic stable and having H∞ performance index are given. Then, the design method of state feedback controller is given to ensure the closed-loop system is stochastic stable and has [Formula: see text] performance index. Finally, simulation examples are given to verify the effectiveness of the proposed methods.

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This paper considers the [Formula: see text] dissipative filtering problem for a class of Singular Markov jump systems (SMJSs) with distributed time delays and discrete time delays. First, using Lyapunov’s stability theory and combining delay partitioning technique, integral partitioning technique, and free weight matrix method, the sufficient conditions for stochastic admissibility and [Formula: see text] dissipation of system are studied. Then, a filtering design method based on linear matrix inequalities (LMIs) is given to make the filtering error system stochastically admissible and [Formula: see text] dissipative. Finally, numerical simulations verify the effectiveness of the resulting method.