A hybrid state-space approach to sampled-data feedback control

Abstract

This paper develops a state-space theory for the study of linear shift-invariant finite-dimensional hybrid dynamical systems. By hybrid systems, we mean an input-output operator relating hybrid signals, that is, signals which consist of two parts: a continuous-time part and a discrete-time part. We first introduce the hybrid state-space model and show the closedness properties under the fundamental operations. We next investigate the standard basic issues associated with this formalism: reachability, observability, and internal stability. We define the notion of H2-norm of the hybrid system and show how to evaluate it. Since the analysis result can be applied to any hybrid system with the proposed hybrid state-space model, we apply the analysis result to the optimal digital control problem for standard four-block configuration with H2-norm performance measure. The solution, with computational algorithm, is derived for the time-delay case.