Dissipative constraint-based control design for singular semi-Markovian jump systems using state decomposition approach

This paper proposes a unified control design for a class of singular semi-Markovian jump systems with a time-varying delay in the state vector by employing the state decomposition approach and dissipative theory. To begin, the addressed system is decomposed into differential–algebraic form with new state vectors, from which a mode-dependent augmented Lyapunov–Krasovskii functional is constructed. The desired stochastic admissibility and dissipative conditions are then obtained, where the auxiliary function-based integral inequality, the generalized free-weighting-matrix approach and the augmented zero equality approach are used in the derivation to achieve less conservative results. In accordance with these conditions, a relationship for determining the mode-dependent gain parameters of the proposed state feedback control is given. As a result, the theoretical findings of this paper lead to better results than some previously published ones, as demonstrated by four numerical examples.