Input-output realization of piecewise affine state space models

This paper addresses the conversion of discrete-time single input-single output piecewise affine (PWA) models from state space to input-output form. Necessary and sufficient conditions are given for a PWA state space model to admit equivalent input-output representations. When an equivalent input-output model exists, a constructive procedure is presented to derive both its parameters and the partition of the regressors domain. It is shown that the number of modes and the number of parameters may grow considerably when converting a PWA state space model into an equivalent input-output representation. Numerical examples highlight the role of the derived necessary and sufficient conditions for input-output realization of PWA state space models.