Robust H_∞ control for a class of quasi‐linear uncertain stochastic time‐varying delayed systems

Abstract

This paper studies the H∞ control for a class of quasi‐linear uncertain stochastic time‐varying delayed systems. Firstly, by using the linear matrix inequality (LMI) method, a sufficient condition is obtained for the robustly stochastic stability. Secondly, the robust H∞ state feedback controller is designed, such that the considered system is not only internally stochastically stabilizable but also satisfies the robust H∞ performance. The desired robust H∞ controller is obtained via solving some LMIs. Finally, one example is provided to demonstrate the effectiveness of the proposed method.

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

“…the ‐gain from the external disturbance to the controlled output is less than a prescribed attenuation level . By choosing an appropriate Lyapunov–Krasovskii functional and employing free‐weighting matrix method, our obtained conditions are less conservative than those of [9].…”

“…iterative learning control [6], filtering problem [7] and consensus control [8]. Time‐delay exists widely in practice and affects the system performance, which often occurs in state [9], control input [10] or measurement output [11]. Time delay might give rise to bifurcation, oscillation, chaos or even instability [12–14].…”

“…It can be found that considerable research interest has been drawn on stochastic delay systems, and various methods in investigating the stochastic stability have been proposed, e.g. the Lyapunov functional/function method combing with the Razumikhin technique or the inequality technique, see [9, 10, 18, 19]. Recently, a new technique named ‐represent technique for stochastic systems was proposed [20] and applied to study the time‐delay systems [21–23].…”

“…In recent 20 years, the stochastic control and stochastic stabilisation have been paid much attention, we refer the reader to the monographs [1, 2, 4, 31], and the references [9, 24, 26–28, 32–34] for time‐delay and/or uncertain stochastic systems. Recently, we studied the control for a class of uncertain stochastic systems with time‐varying delays and non‐linear perturbations [9]. Nevertheless, the obtained conditions have more conservatism due to the handling method used in [9].…”

“…Recently, we studied the control for a class of uncertain stochastic systems with time‐varying delays and non‐linear perturbations [9]. Nevertheless, the obtained conditions have more conservatism due to the handling method used in [9]. In order to obtain new less conservative criteria for time‐delay systems, some useful methods were proposed such as transformation technique [35], free‐weighting matrix method [15], integral inequality technique [36] and delay decomposition [37].…”