Closed loop stability of a class of non-linear singularly perturbed systems with discretized composite feedback

In this paper, we investigate the digital implementation of continuous-time composite control feedback for a class of non-linear singularly perturbed systems. Although starting with a stabilizing control feedback, the sampling process may destroy the stability properties of the resulting closed-loop system. In this paper, multirate measurements (slow variables are measured at a rate slower than that of fast variables) are considered. Sufficient conditions for the slow and fast sampling periods which preserve exponential stability properties are established. Finally, a numerical example is given to illustrate the theoretical results.