Finite-time dissipative control for discrete-time stochastic delayed systems with Markovian switching and interval parameters

The problem of finite-time dissipative control for discrete-time stochastic delayed systems (DTSDSs) with Markovian switching and interval parameters is studied in this paper. Firstly, DTSDSs are equivalently transformed into discrete-time uncertain stochastic delayed systems, whose interval parameters are described by a series of convex combinations of the endpoints information. Then, finite-time stochastic boundedness (FTSB) and finite-time stochastic exponential ( Q i , S i , R i ) − α dissipative (FTSED) are analysed by constructing a discrete-time Lyapunov–Krasovskii functional. Correspondingly, several sufficient conditions are obtained in terms of Linear Matrix Inequalities (LMIs). Furthermore, the delay-feedback controllers with memory are designed such that the finite-time dissipative performance of the DTSDSs is satisfied. Finally, the proposed results are validated through a switching energy-storing electrical circuit. • We consider a class of stochastic delayed systems with Markovian switching. • The interval matrix method is used to reduce the computational complexity. • Based on the Schur complement and LMIs, several conditions for FTSED are obtained. • The finite-time dissipative state feedback controllers with memory are adopted.