Non-fragile observer-based H∞H∞ control for stochastic time-delay systems

This paper considers the problem of non-fragile observer-based H∞H∞ control for stochastic time-delay systems. The controller and observer to be designed are assumed to have norm-bounded gain perturbations. By choosing an appropriate Lyapunov–Krasovskii functional and introducing a slack matrix variable, a less conservative delay-dependent condition of exponential stability in mean square is presented in the form of linear matrix inequalities (LMIs). A stochastic bounded real lemma is then established. On the basis of this, a new LMI-based approach is developed for designing non-fragile observer-based H∞H∞ controllers without imposing any constraints on the system matrices. Finally, two numerical examples are provided to demonstrate the effectiveness and reduced conservatism of the proposed design approach.