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Stability results for some classes of cooperative systems

Author
Organization
Abstract
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. Additionally a stability result for a particular class of Kolmogorov systems is established. We compare our main results to those in the literature.
Keywords
DIFFERENTIAL-EQUATIONS

Citation

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MLA
De Leenheer, Patrick, and Dirk Aeyels. “Stability Results for Some Classes of Cooperative Systems.” Ieee Conference on Decision and Control - Proceedings. New York, NY, USA: IEEE, 2000. 2965–2970. Print.
APA
De Leenheer, P., & Aeyels, D. (2000). Stability results for some classes of cooperative systems. IEEE CONFERENCE ON DECISION AND CONTROL - PROCEEDINGS (pp. 2965–2970). Presented at the 39th IEEE Conference on Decision and Control, New York, NY, USA: IEEE.
Chicago author-date
De Leenheer, Patrick, and Dirk Aeyels. 2000. “Stability Results for Some Classes of Cooperative Systems.” In Ieee Conference on Decision and Control - Proceedings, 2965–2970. New York, NY, USA: IEEE.
Chicago author-date (all authors)
De Leenheer, Patrick, and Dirk Aeyels. 2000. “Stability Results for Some Classes of Cooperative Systems.” In Ieee Conference on Decision and Control - Proceedings, 2965–2970. New York, NY, USA: IEEE.
Vancouver
1.
De Leenheer P, Aeyels D. Stability results for some classes of cooperative systems. IEEE CONFERENCE ON DECISION AND CONTROL - PROCEEDINGS. New York, NY, USA: IEEE; 2000. p. 2965–70.
IEEE
[1]
P. De Leenheer and D. Aeyels, “Stability results for some classes of cooperative systems,” in IEEE CONFERENCE ON DECISION AND CONTROL - PROCEEDINGS, Sydney, Australia, 2000, pp. 2965–2970.
@inproceedings{401861,
  abstract     = {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. Additionally 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},
  booktitle    = {IEEE CONFERENCE ON DECISION AND CONTROL - PROCEEDINGS},
  isbn         = {0-7803-6638-7},
  issn         = {0191-2216},
  keywords     = {DIFFERENTIAL-EQUATIONS},
  language     = {eng},
  location     = {Sydney, Australia},
  pages        = {2965--2970},
  publisher    = {IEEE},
  title        = {Stability results for some classes of cooperative systems},
  year         = {2000},
}

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