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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:

93C05 Linear systems in control theory
93B03 Attainable sets, reachability
93B05 Controllability
26A33 Fractional derivatives and integrals
15B48 Positive matrices and their generalizations; cones of matrices
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