GLOBAL INPUT-TO-STATE STABILITY AND STABILIZATION OF DISCRETE-TIME PIECE-WISE AFFINE SYSTEMS

This paper presents sufficient conditions for global Input-to-State (practical) Stability (ISpS) and stabilization of discrete-time, possibly discontinuous, Piece-Wise Affine (PWA) systems. Piece-wise quadratic candidate ISpS (ISS) Lyapunov functions are employed for both analysis and synthesis purposes. This enables us to obtain sufficient conditions based on linear matrix inequalities, which can be solved efficiently. One of the advantages of using the ISpS framework is that the additive disturbance inputs are explicitly taken into account in the analysis and synthesis procedures, and the results apply to PWA systems in their full generality, i.e. non-zero affine terms are allowed in the regions in the partition whose closure contains the origin.