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Positivity and stabilization of 2D linear systems. (English) Zbl 1206.93085

Summary: The problem of finding a gain matrix of the state-feedback of 2D linear system such that the closed-loop system is positive and asymptotically stable is formulated and solved. Necessary and sufficient conditions for the solvability of the problem are established. It is shown that the problem can be reduced to a suitable linear programming problem. The proposed approach can be extended to 2D linear system described by the 2D Roesser model.

MSC:

93D15 Stabilization of systems by feedback
93C05 Linear systems in control theory
93D20 Asymptotic stability in control theory
90C05 Linear programming
93B52 Feedback control
15B48 Positive matrices and their generalizations; cones of matrices
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