Classification of linear planar systems with hybrid feedback control

Continuing the authors’ studies of hybrid dynamical systems, i.e. differential equations governed by finite automata, an efficient and complete classification of control linear systems in the plane is offered. The set of all such systems is divided into equivalence classes which are explicitly characterized by some quantitative invariants. The canonical representatives in each class are determined. It is shown how to use this classification to find out whether a given system is stabilizable or not.