Advanced search
1 file | 213.55 KB

Stability properties of equilibria of classes of cooperative systems

Author
Organization
Abstract
This note deals with the constant control problem for homogeneous cooperative and irreducible systems. These systems serve as models for positive systems. A necessary and sufficient condition for global asymptotic stability of the zero solution of this class of systems is known. Adding a constant control allows to shift the equilibrium point from zero to a point in the first orthant. We prove that for every nontrivial nonnegative control vector a unique nontrivial equilibrium point is achieved which is globally asymptotically stable if the zero solution of the uncontrolled system is globally asymptotically stable. In addition a converse result is provided. Finally a stability result for a particular class of Kolmogorov systems is established. We compare our main results to those in the literature.
Keywords
positive systems, cooperative systems, stability

Downloads

  • (...).pdf
    • full text
    • |
    • UGent only
    • |
    • PDF
    • |
    • 213.55 KB

Citation

Please use this url to cite or link to this publication:

Chicago
De Leenheer, Patrick, and Dirk Aeyels. 2001. “Stability Properties of Equilibria of Classes of Cooperative Systems.” Ieee Transactions on Automatic Control 46 (12): 1996–2001.
APA
De Leenheer, P., & Aeyels, D. (2001). Stability properties of equilibria of classes of cooperative systems. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 46(12), 1996–2001.
Vancouver
1.
De Leenheer P, Aeyels D. Stability properties of equilibria of classes of cooperative systems. IEEE TRANSACTIONS ON AUTOMATIC CONTROL. 2001;46(12):1996–2001.
MLA
De Leenheer, Patrick, and Dirk Aeyels. “Stability Properties of Equilibria of Classes of Cooperative Systems.” IEEE TRANSACTIONS ON AUTOMATIC CONTROL 46.12 (2001): 1996–2001. Print.
@article{144471,
  abstract     = {This note deals with the constant control problem for homogeneous cooperative and irreducible systems. These systems serve as models for positive systems. A necessary and sufficient condition for global asymptotic stability of the zero solution of this class of systems is known. Adding a constant control allows to shift the equilibrium point from zero to a point in the first orthant. We prove that for every nontrivial nonnegative control vector a unique nontrivial equilibrium point is achieved which is globally asymptotically stable if the zero solution of the uncontrolled system is globally asymptotically stable. In addition a converse result is provided. Finally a stability result for a particular class of Kolmogorov systems is established. We compare our main results to those in the literature.},
  author       = {De Leenheer, Patrick and Aeyels, Dirk},
  issn         = {0018-9286},
  journal      = {IEEE TRANSACTIONS ON AUTOMATIC CONTROL},
  keywords     = {positive systems,cooperative systems,stability},
  language     = {eng},
  number       = {12},
  pages        = {1996--2001},
  title        = {Stability properties of equilibria of classes of cooperative systems},
  url          = {http://dx.doi.org/10.1109/9.975508},
  volume       = {46},
  year         = {2001},
}

Altmetric
View in Altmetric
Web of Science
Times cited: