Finite-time interval stabilization for time-varying stochastic delayed systems via interval matrix method by piecewise controllers

Abstract

This paper presents a comprehensive study addressing the problem of finite-time interval stabilization (FTIS) for two distinct types of systems: linear time-invariant stochastic delayed systems (LTISDSs) and linear time-varying stochastic delayed systems (LTVSDSs). To begin, the definition of FTIS is established, which is based on employing piecewise state feedback controllers. Subsequently, a time-varying Lyapunov-Krasovskii functional (LKF) is proposed and a novel optimization algorithm is designed to address the challenge of FTIS for LTISDSs. Additionally, this paper investigates the equivalence of LTVSDSs to uncertain stochastic delayed systems with interval parameters, represented as a series of convex combinations. Notably, both the optimization algorithm and the linear matrix inequalities (LMIs) technique are employed to establish sufficient conditions for achieving FTIS in LTVSDSs. Furthermore, when compared to traditional state feedback controllers, the piecewise controllers not only enhance the precision of system control but also lead to reduced control gains and fewer control effort requirements. Finally, the findings are substantiated through the presentation of two numerical examples, providing practical validation for the proposed methodologies and their effectiveness.