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.(c) 2022 Elsevier Ltd. All rights reserved.