Observations on the stability properties of cooperative systems

Systems and Control Letters - Tập 58 Số 6 - Trang 461-467 - 2009
Oliver Mason1, Mark Verwoerd1
1Hamilton Institute, National University of Ireland, Maynooth, Co., Kildare, Ireland

Tóm tắt

Từ khóa


Tài liệu tham khảo

Farina, 2000

Berman, 1994

Bru, 2000, Canonical forms for positive discrete-time linear control systems, Linear Algebra and its Applications, 310, 49, 10.1016/S0024-3795(00)00044-6

Valcher, 1996, Controllability and reachability criteria for discrete-time positive systems, International Journal of Control, 65, 511, 10.1080/00207179608921708

Benvenuti, 2004, A tutorial on the positive realization problem, IEEE Transactions on Automatic Control, 49, 651, 10.1109/TAC.2004.826715

de Leenheer, 2001, Stability properties of equilibria of classes of co-operative systems, IEEE Transactions on Automatic Control, 46, 1996, 10.1109/9.975508

Haddad, 2004, Stability theory for nonnegative and compartmental dynamical systems with time delay, Systems and Control Letters, 51, 355, 10.1016/j.sysconle.2003.09.006

Smith, 1995

Hirsch, 1985, Systems of differential equations that are competitive or cooperative. ii: Convergence almost everywhere, SIAM Journal of Mathematical Analysis, 16, 423, 10.1137/0516030

de Leenheer, 2002, Extension of the Perron–Frobenius theorem to homogeneous systems, SIAM Journal of Control and Optimization, 41, 563, 10.1137/S0363012900361178

Angeli, 2004, Multi-stability in monotone input/output systems, Systems and Control Letters, 51, 185, 10.1016/j.sysconle.2003.08.003

Angeli, 2003, Monotone control systems, IEEE Transactions on Automatic Control, 48, 1684, 10.1109/TAC.2003.817920

Haddad, 2005, Stability and dissipativity theory for nonnegative dynamical systems: A unified analysis framework for biological and physiological systems, Nonlinear Analysis: Real World Applications, 6, 35, 10.1016/j.nonrwa.2004.01.006

Haddad, 2006, Adaptive control for nonlinear compartmental dynamical systems with applications to clinical pharmacology, Systems and Control Letters, 55, 62, 10.1016/j.sysconle.2005.05.002

Ngoc, 2006, A Perron–Frobenius theorem for a class of positive quasi-polynomial matrices, Applied Mathematics Letters, 19, 747, 10.1016/j.aml.2005.10.005

Hale, 1993

J. Szarski, Differential Inequalities, Monographie Matematyczne, Warsaw, 1965

Morishima, 1964

Nussbaum, 1988

Gaubert, 2004, The Perron–Frobenius theorem for homogeneous monotone functions, Transactions of the American Mathematical Society, 356, 4931, 10.1090/S0002-9947-04-03470-1

Horn, 1985

S. Dashkovskiy, B. Rüffer, F. Wirth, An ISS small-gain theorem for general networks, Technical Report 2005-05, Zentrum für Technomathematik, Universiteit Bremen, 2005

Lui, 1989, Biological growth and spread modeled by systems of recursions i. mathematical theory, Mathematical Biosciences, 93, 269, 10.1016/0025-5564(89)90026-6