SIMPLE ASYMPTOTIC STABILIZING CONTROL LAWS FOR LINEAR TIME-INVARIANT HYBRID SYSTEMS

Abstract

This paper deals with the derivation of simple asymptotically stabilizing control laws for linear time-invariant hybrid systems, namely those that consist, in general, of coupled continuous-time and digital and or discretetime ones. The design philosophy consists of two steps. First, the synthesis of an asymptoticallystabilizing control law for the hybrid system at sampling instants is performed through the derivation of an auxiliary extended discrete system. Such a system contains both the digital substate and the discretization at sampling instants of the continuous-time substate. Subsequently, an incremental control law, which acts in between sampling instants, is synthesized to ensure the maintenance of global asymptotic stability during the intersample interval. The synthesis of the incremental control is based on small-gain type arguments related to the incremental controller. The related stability analysis is performed with the natural extension of the description on the intersample intervals of the state trajectory of the auxiliary extended system. Special emphasis is given to the use of multirate sampling as a tool for the synthesis of globally asymptotically stabilizing controls. Multirate control is an important tool to accommodate sampling of different signals in the loop at their natural sampling rates and also for noise-filtering purposes see, for instance Berg et al., 1986a; De la Sen, 1986a, 1996a, 1996b . In particular, faster input input and output sampling is shown to relax the conditions for asymptotic stabilization at sampling instants through state output feedback.