Stability and contractivity of conewise linear systems

This work investigates stability of conewise linear systems. By introducing the concept of unit-sphere piecewise contractivity with respect to a given norm, we establish the equivalence between exponential stability and unit-sphere piecewise contractivity with respect to any norm. As an implication, we present a veri£able stability criterion based on state simulation and reduce-order unit ball coverage veri£cation. The approach applies to both continuous-time and discrete-time systems.