A novel approach to state bounding for discrete-time Markovian jump systems with interval time-varying delay

This paper concerns with the problem of state bounding for a class of discrete-time Markovian jump systems with interval time-varying delay. By constructing a new Lyapunov–Krasovskii functional combining with the delay-decomposition technique and the reciprocally convex approach, new delay-range-dependent conditions are derived ensuring that all state trajectories of the system are mean square bounded. These conditions are derived in terms of matrix inequalities which can be computationally solved to find a smallest possible bound of mean square. A numerical example is provided to verify the effectiveness of the obtained result.