State estimation and stabilization of nonlinear systems with sampled-data control and uncertain disturbances

We consider continuous-time sampled-data control systems with uncertain nonlinearities subject to bounded exogenous disturbances. Based on the method of quadratic Lyapunov functions, matrix comparison systems, and the technique of differential linear matrix inequalities, an approach is developed to problems of state estimation and rejection of initial deviations and uncertain disturbances using sampled-data state feedback. A method is proposed for the synthesis of a periodic and an aperiodic sampled-data control ensuring that the trajectories of the original system on a finite horizon lie in a given set under any disturbances bounded in the $L_\infty $ -norm.