Coupling of stable subsystems with counterclockwise input-output dynamics

Counterclockwise input-output dynamics, a stability notion introduced by Angeli, enables convergence analysis of the positive feedback interconnection in a way similar to that of the negative feedback interconnection of two passive subsystems. In this paper, we consider internal stability for a ring of (possibly arbitrarily many) coupled stable subsystems through positive feedback interconnections, where each subsystem is equipped with counterclockwise input-output dynamics. Sufficient conditions on inter-subsystem coupling gains and DC gains are derived for guaranteeing internal stability of the ring. The derived stability results avoid explicit computation of eigenvalues or construction of Lyapunov functions.