Non‐fragile robust exponential stabilisation and control for uncertain stochastic systems with non‐linearity and mixed delays

Abstract

This study focuses on the delay-dependent robust exponential stabilisation and H ∞ control for uncertain stochastic time-delay systems with non-linear terms. Uncertain parameters are assumed to be time-varying norm bounded, while time-varying delay terms include both discrete and distributed delays. Firstly, by choosing an appropriate Lyapunov–Krasovskii functional, a sufficient condition for the robust exponential stabilisation is obtained. Secondly, the H ∞ control is also discussed. All criteria are presented in the form of linear matrix inequalities with less conservatism. Finally, an example verifies the validity of the proposed method.