Classification and stabilizability analysis of bimodal piecewise affine systems

This paper presents a classification of bimodal piecewise affine systems from the viewpoint of well-posedness. First, we address the problem of feedback equivalence to a well-posed system, called here the feedback well-posedness problem, of a general class of bimodal piecewise affine systems. Next, based on this result, we classify all feedback well-posed systems into four classes to address the control problem of piecewise affine systems in a systematic way. Finally, as its application, the stabilizability with well-posedness is discussed for each class, and several remarks on stabilizability are given