Robust Exponential Stabilization for Sampled-Data Systems with Variable Sampling and Packet Dropouts

This paper investigates the problem of robust exponential stabilization for sampled-data systems with variable sampling and packet dropouts. It is assumed that the system parameter uncertainties are norm-bounded and appear in both the state and input matrices. An input delay approach is adopted to model the sample-and-hold behavior with a time-varying delayed control input, and a switched system approach is proposed to model the data-missing phenomenon. On this basis, the sampled-data control system with variable sampling and packet dropouts is modeled as a switched system with time-varying delay. The objective is to design a sampled-data controller to guarantee the robust exponential stability of the resulting closed-loop system. Based on a new piecewise time-dependent Lyapunov functional, novel sufficient conditions are derived for the existence of robustly exponentially stabilizing sampled-data controllers. It is shown that the controller gains can be obtained by solving a set of linear matrix inequalities. Two simulation examples are given to demonstrate the effectiveness of the proposed method.