Robust $$H_\infty $$H∞ Repetitive Control for a Class of Linear Stochastic Switched Systems with Time Delay

This paper investigates the problem of robust $$H_\infty $$H∞ repetitive control for a class of linear stochastic switched systems with time delay. Based on the lifting technique, a continuous-discrete stochastic 2D (two-dimensional) delayed model is firstly proposed to describe the control and learning actions of the repetitive control system. Then a sufficient condition for the asymptotical stability with $$H_\infty $$H∞ performance of the 2D model is derived by choosing an appropriate common Lyapunov functional. The feedback controller gains are then obtained by solving a set of linear matrix inequalities. One example is given to illustrate the effectiveness of the proposed method.

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