On stabilizability-holdability problem for linear discrete time systems

• Autorzy: Rumchev V., G. , Higashiyama Y.
• Języki publikacji: EN

Abstrakty

EN

Consider the following problem. Given a linear discrete-time system, find if possible a linear state-feedback control law such that under this law all system trajectories originating in the non-negative orthant remain non-negative while asymptotically converging to the origin. This problem is called feedback stabilizability-holdabiltiy problem (FSH). If, in addition, the requirement of non-negativity is imposed on the controls, the problem is a positive feedback stabilizability-holdabiltiy problem (PFSH). It is shown that the set of all linear state feedback controllers that make the open-loop system holdable and asymptotically stable is a polyhedron and the external representation of this polyhedron is obtained. Necessary and sufficient conditions for identifying when the open-loop system is not positive feedback R+n-invariant (and therefore there is no solution to the PFSH problem) are obtained in terms of the system parameters. A constructive linear programming based approach to the solution of FSH and PFSH problems is developed in the paper. This approach provides not only a simple computational procedure to find out whether the FSF, respectively the PFSH problem, has a solution or not but also to determine a linear state feedback controller (respectively, a non-negative linear state feedback controller) that endows the closed-loop (positive) system with a maximum stability margin and guarantees the fastest possible convergence to the origin.

Słowa kluczowe

EN

positive systems; non-negative matrices; linear discrete time systems; positively invariant sets; feedback invariance; stabilizability

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Systems Science
• Rocznik: 2010
• Tom: Vol. 36, no 2
• Strony: 33--38
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Rumchev V., G.

autor

Higashiyama Y.

• Department of Mathematics and Statistics, Curtin University of Technology, GPO Box U 1987, Perth, WA 6845, Perth, Australia,

Bibliografia

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