OBSERVER DESIGN FOR A CLASS OF DISCRETE TIME PIECEWISE-LINEAR SYSTEMS

In this paper we consider a class of discrete time piecewise-linear systems composed by linear discrete time LTI subsystems with autonomous switching. The aim is to propose a method for the synthesis of a hybrid observer. The approach proposed here consists on the combination of a discrete observer and a continuous observer. It is shown that under conditions related to minimum dwell time of each mode, one can express the switching law as a linear combination of the system input/output samples. The continuous observer is a piecewise-linear observer whose dynamics depend on the current active mode. Two estimation schemes are analyzed : on-line estimation and off-line estimation.