Extended dissipativity-based finite-time control of Markov jump systems with state and mode detection delays

This article is concerned with the extended dissipativity-based finite-time control of the continuous-time Markov jump systems with state and mode detection delays. The mode detection delay implies a lag between system and controller modes. First, we assume that the mode detection delay of the controller obeys an exponential distribution. Based on an augmented mode signal, the Markov jump systems with state and mode detection delays are remodeled as standard Markov jump systems, whose transition rate matrix depends on the transition rate of the original system mode and the exponential distribution rate of the mode detection delay. The remodeled system with and without mode detection delay corresponds to the synchronization and asynchronization of the system and controller modes, respectively, which is more general than existing results. Subsequently, a novel delay-product-type Lyapunov–Krasovskii functional that contains delay integral and non-integral terms is constructed. The generalized free-matrix-based integral inequality estimates the delay integral terms in the Lyapunov–Krasovskii functional derivatives, yielding the less conservative finite-time stochastically stable, finite-time stochastically bounded, and extended dissipative finite-time stochastically bounded criteria. A state-feedback controller is further designed to ensure the underlying systems are extended dissipative finite-time stochastically bounded. By choosing suitable parameters, the extended dissipative finite-time stochastically bounded criterion can be reduced to various performance criteria, and the existing results are special cases of this article. Finally, a numerical example and a boost converter circuit are provided to verify the validity and applicability of the proposed methods.