Robust H∞ Control for Uncertain Nonlinear Stochastic Systems with Delayed State and Control
This paper considers the issue of robust H∞ control for a class of nonlinear uncertain systems with delayed states and control, and the feedback controller is designed. By constructing proper Lyapunov-krasovskii function, the resulting closed-loop system is stochastically stable for all admissible uncertainties, time-delays and nonlinearities, and satisfies a prescribed H∞ performance. Sufficient conditions for the system to be robustly stochastically asymptotically stable are derived, by using linear matrix inequalities and Lyapunov-krasovskii stability theory. The feedback controller is obtained by solving the linear matrix inequalities. Numerical example is provided to show the validity of the proposed approaches.
C. Wang and Y. Xu, "Robust H∞ Control for Uncertain Nonlinear Stochastic Systems with Delayed State and Control", Applied Mechanics and Materials, Vols. 58-60, pp. 685-690, 2011