State Estimation for a Class of Discrete-Time Piecewise-Linear Systems

In this paper, we investigate the problem of state estimation of a class of hybrid 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 proposed approach consists in combining a discrete observer with a continuous observer. It is shown that under conditions related to minimum dwell time of each mode, the switching law can be expressed 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.