On the robust stability and stabilization of sampled-data systems: A hybrid system approach

Abstract

We consider the stability analysis and state-feedback stabilization of LTI uncertain sampled-data systems. There are two sources of uncertainty: the plant's parameters can be uncertain and the sampling intervals can be unknown and variable. We model the sampled-data system as a hybrid system and we employ a Lyapunov function with discontinuities to establish the stability of the system. Our stability and stabilization results are presented as Linear Matrix Inequalities (LMIs). By solving these LMIs, one can find a positive constant which determines an upper bound on the sampling intervals such that the stability of the closed-loop is guaranteed. The control design LMIs also provide controller gains that can be used to stabilize a given process. To reduce the conservativeness we use slack matrices; however, we require a smaller number of slack matrices than in the previous results and we show that we have done it without making the results more conservative. As a special case we consider sampled-data systems with constant sampling intervals and provide results for this class of systems that are less conservative than the ones obtained for the general case of variable sampling time.