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.


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
Full Text: DOI


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