Finite-Time Stability Analysis and Stabilization of Discrete-Time Stochastic Time-Varying Systems with Time Delay via the Interval-Matrix Method

This paper investigates the finite-time stochastic stability (FTSS) and stabilization of discrete-time stochastic time-varying systems (DSTSs) with time delay. Within the framework of differential inclusions, the DSTSs are first transformed into systems with interval parameters. Utilizing novel Lyapunov-Krasovskii function (LKF) and linear matrix inequalities(LMIs), sufficient conditions for FTSS of the systems are proposed. Additionally, by applying state feedback, suitable controllers are designed to achieve finite-time stabilization of the systems. However, this approach unavoidably introduces conservatism, leading to increased control costs and energy consumption. Therefore, we propose a new piecewise control method to reduce control costs. Finally, simulation examples are provided to demonstrate the effectiveness and applicability of the proposed approach.