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On positively invariant polyhedrons for continuous-time positive linear systems. (English) Zbl 1454.93115
Summary: This paper is concerned with the determination of positively invariant polyhedron for positive linear systems subject to external disturbances whose $$(\infty,1)$$-norm or $$(\infty,\infty)$$-norm are bounded by a prescribed constant. Necessary and sufficient conditions for the existence of a positively invariant polyhedron are derived in terms of a set of inequalities which can be solved by linear programming, and the link between Lyapunov stability and positively invariant polyhedron is also revealed.
##### MSC:
 93C28 Positive control/observation systems 93C05 Linear systems in control theory 93C73 Perturbations in control/observation systems 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory 90C05 Linear programming
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