Observer design for a class of piecewise linear systems

In this paper we present observer design procedures for a class of bi-modal piecewise linear systems in both continuous and discrete time. We propose Luenberger-type observers, and derive sufficient conditions for the observation error dynamics to be globally asymptotically stable, in the case when the system dynamics is continuous over the switching plane. When the dynamics is discontinuous, we derive conditions that guarantee that the relative estimation error with respect to the state of the observed system will be asymptotically small. The presented theory is illustrated with several examples.