Monotone Control Systems

Monotone Control Systems (2003)

Cached

Download Links

by David Angeli , Eduardo D. Sontag

Citations:

BibTeX

@MISC{Angeli03monotonecontrol,
    author = {David Angeli and Eduardo D. Sontag},
    title = {Monotone Control Systems},
    year = {2003}
}

Years of Citing Articles

Bookmark

OpenURL

Abstract

Monotone systems constitute one of the most important classes of dynamical systems used in mathematical biology modeling. The objective of this paper is to extend the notion of monotonicity to systems with inputs and outputs, a necessary first step in trying to understand interconnections, especially including feedback loops, built up out of monotone components. Basic definitions and theorems are provided, as well as an application to the study of a model of one of the cell's most important subsystems.

Citations

286	Mathematical Control Theory: Deterministic Finite Dimensional Systems. Second Edition - Sontag - 1998
203	From molecular to modular cell biology - Hartwell, Hopfield, et al. - 1999
145	Introduction Dynamic Systems: Theory, Models & Applications - Luenberger - 1979
136	Small gain theorems for ISS systems and applications - Jiang, Teel, et al. - 1994
121	Nonsmooth Analysis and Control Theory - Clarke, Ledyaev, et al. - 1998
120	Monotone Dynamical Systems. An Introduction to the Theory of Competitive and Cooperative Systems - Smith - 1995
69	Ultrasensitivity in the mitogen-activated protein kinase cascade - Huang, Ferrell - 1996
57	Output-to-state stability and detectability of nonlinear systems - Sontag, Wang
49	Detection of multistability, bifurcations, and hysteresis in a large class of biological positive-feedback systems - Angeli, Ferrell, et al. - 2004
45	Negative feedback and ultrasensitivity can bring about oscillations in the mitogen-activated protein kinase cascades - Kholodenko - 2000
39	Stability theory by Liapunov’s direct method - Rouche, Habets, et al. - 1977
34	Remarks on stabilization and input-to-state stability - Sontag - 1989
32	A Lyapunov approach to incremental stability properties - Angeli
30	Positive Linear Systems: Theory and Applications - Farina, Rinaldi - 2000
26	On the differential equations of species in competition - Smale - 1976
25	Differential equations and convergence almost everywhere in strongly monotone flows - Hirsch - 1983
22	Cross-positive matrices - Schneider, Vidyasagar - 1970
21	New characterizations of input to state stability - Sontag, Wang - 1996
19	Asymptotic amplitudes and Cauchy gains: a small-gain principle and an application to inhibitory biological feedback - Sontag
15	An infinite-time relaxation theorem for differential inclusions, to appear - Ingalls, Sontag, et al.
12	Stabilization of positive linear systems - Leenheer, Aeyels
11	Remarks on excitability, stability, and sign of equilibria in cooperative systems - Piccardi, Rinaldi - 2002
10	A remark on the converging-input converging-state property,” preprint arXiv math.OC/0205016, May 2002, and submitted - Sontag
10	Gewohnliche differentialungleichungen mit quasimonoton wachsenden funktionen in topologischen vektorraumen - Volkmann - 1972
9	Existence of nontrivial unstable sets for equilibriums of strongly order-preserving systems - Matano - 1984
8	Controllability and reachability criteria for discrete-time positive systems,” Int - Valcher - 1996
6	A feedback perspective for chemostat models with crowding effects. Lect - Leenheer, Angeli, et al.
5	Leenheer, “Stability for homogeneous cooperative systems - Aeyels, De - 1999
5	Stability properties of equilibria of classes of cooperative systems - Leenheer, Aeyels - 2001
4	Stability results for some classes of cooperative systems - Leenheer, Aeyels - 2000
4	Filippov, Di#erential Equations with Discontinuous Righthand Sides - F - 1988
3	Positive Linear Systems:Theory and Applications - Farina, Rinaldi - 2000
3	A proof of the two-dimensional Markus-Yamabe conjecture - Fessler - 1995
3	Excitability, stability, and sign of equilibria in positive linear systems - Muratori, Rinaldi - 1991
2	Further remarks on monotone systems with inputs and outputs - Angeli, Sontag
2	Systems of differential equations that are competitive or cooperative II: convergence almost everywhere - Hirsh - 1985
2	Monotonicity with respect to closed convex cones II, Applicable Analysis 77 - Kunze, Siegel - 2001
2	Flow-invariant sets and differential inequalities in normed spaces - Redheffer, Walter - 1975
2	David Angeli received the degree in computer science engineering and the Ph.D. degree from the University of Florence - Berlin - 1970
1	Small-gain theorems for predator-prey systems - Leenheer, Angeli, et al. - 2003
1	Systems of dierential equations that are competitive or cooperative II: Convergence almost everywhere - Hirsh - 1985
1	An in relaxation theorem for dierential inclusions - Ingalls, Sontag, et al.
1	feedback perspective for chemostat models with crowding effects,” presented at the 1st Multidisciplinary Int - “A - 2003
1	Positive control for quasimonotone systems of differential equations - Sachs - 1981
1	remark on the converging-input converging-state property - “A - 2003