Stability properties of equilibria of classes of cooperativesystems |
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Authors: | De Leenheer P Aeyels D |
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Affiliation: | Dept. of Math., Arizona State Univ., Tempe, AZ ; |
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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 |
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