Switched feedback equivalence of a class of planar switched nonlinear systems

This paper presents a new concept of linearization of switched nonlinear systems, called modal feedback linearization. The aim is to transform a switched nonlinear system into an equivalent controllable switched linear system. First, we define the notion of modal state feedback linearization. Then, we present a class of planar switched nonlinear systems which are globally transformable by a switched state feedback control and a state space transformation into a controllable switched linear system. Necessary and sufficient conditions are given for the existence of a suitable state transformation with a special structure. Our approach is constructive in nature in the sense that once the conditions are satisfied, the state transformation is derived leading to modal feedback linearization. Two illustrative examples, including a physical one, are presented.