On graphs, conic relations, and input-output stability of nonlinear feedback systems

This paper presents necessary and sufficient conditions for the stability of general interconnected dynamical systems. The results are expressed in terms of the graphs of the interconnection's subsystems. Conditions for robustness of stability for an interconnection with additive disturbances are also provided. Finally, the paper gives sufficient conditions for stability using conic sector conditions that generalize earlier conditions and that incorporate a recent nonlinear small gain idea.