Passivity gains and the “secant condition” for stability

M. Arcak, E.D. Sontag, Diagonal stability for a class of cyclic systems and applications, submitted for publication. De Leenheer, 2001, Stabilization of positive linear systems, Systems Control Lett., 44, 259, 10.1016/S0167-6911(01)00146-3 Desch, 2001, Meagre functions and asymptotic behaviour of dynamical systems, Nonlinear Anal., 44, 1087, 10.1016/S0362-546X(99)00323-5 Farina, 2000 Khalil, 1996 Mallet-Paret, 1990, The Poincaré–Bendixson theorem for monotone cyclic feedback systems, J. Dynamics Differential Equations, 2, 367, 10.1007/BF01054041 Megretski, 1997, System analysis via integral quadratic constraints, IEEE Trans. Automat. Control, 47, 819, 10.1109/9.587335 Saeks, 1970, Causality in Hilbert space, SIAM J. Control, 12, 357 Sontag, 1990 Sontag, 2002, Asymptotic amplitudes and Cauchy gains: a small-gain principle and an application to inhibitory biological feedback, Systems Control Lett., 47, 167, 10.1016/S0167-6911(02)00191-3 Thron, 1991, The secant condition for instability in biochemical feedback control. I. The role of cooperativity and saturability, Bull. Math. Biol., 53, 383 Tyson, 1978, The dynamics of feedback control circuits in biochemical pathways, vol. 5, 1 van der Schaft, 2000 Vidyasagar, 1978