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Positive 2D fractional linear systems. (English) Zbl 1173.93017
Summary: The purpose of this paper is to introduce a new class of positive two-dimensional (2D) fractional linear systems. A notion (concept) of order 2D difference is proposed and the solution to the state equations is given. The classical Cayley-Hamilton theorem is extended to the positive 2D fractional linear systems. Necessary and sufficient conditions for the positivity of 2D fractional linear systems, reachability and controllability to zero are established. A method for analysis of positive 2D fractional linear systems is proposed.

MSC:
93C05Linear control systems
93B03Attainable sets
93B05Controllability
26A33Fractional derivatives and integrals (real functions)
15B48Positive matrices and their generalizations; cones of matrices
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