Finite-time piecewise control for discrete-time stochastic nonlinear time-varying systems with time-varying delays

This study delves into the analysis and control of finite -time stochastic stability (FTSS) within discrete stochastic nonlinear time -varying systems (DSNTSs) with time -varying delays. Leveraging set -valued mappings and incorporating principles from differential inclusion theory, the DSNTSs are transformed into a set of differential inclusion subsystems, introducing a novel approach to system control. Sufficient conditions for FTSS are established through the introduction of discrete -time Lyapunov-Krasovskii functions and the application of linear matrix inequalities (LMIs). To ensure the FTSS of the systems, we introduce a set of piecewise state feedback controllers. In addition, we propose an optimized control algorithm founded on piecewise control, designed to enhance the overall cost-effectiveness. The efficacy of these methodological innovations is fully validated by a series of comprehensive numerical simulations.