Two approaches to state estimation for a class of piecewise affine systems

In this paper we present two approaches to state estimation for a class of discrete time bi-modal piece-wise affine systems. The proposed approaches have the characteristic feature that they do not require information on the currently active dynamics of the piecewise affine system. We propose a Luenberger-type observer, and derive sufficient conditions for the observation error 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 estimation error will be bounded with respect to the state bound. Second, we propose to apply particle filtering algorithm, which aims at approximating the a posteriori probability density of the state. The presented approaches are compared and illustrated with examples.