Observer design for a class of piece-wise affine systems

In this paper we propose an observer design procedure for a class of bi-modal piece-wise affine systems. The designed observers have the characteristic feature that they do not require information on the currently active dynamics of the piecewise linear system. A design procedure which guarantees global asymptotic stability of the estimation error is presented. It is shown that the applicability of the presented procedure is limited to continuous piece-wise affine systems. Therefore, we present an observer design procedure, applicable also to discontinuous systems, which guarantees that the estimation error is bounded, with respect to the state bounds, asymptotically. Sliding motions in the observed system, and the observer are discussed. The presented theory is illustrated with an example.