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Positivity and stabilization of fractional 2D linear systems described by the Roesser model. (English) Zbl 1300.93136

Summary: A new class of fractional 2D linear discrete-time systems is introduced. The fractional difference definition is applied to each dimension of a 2D Roesser model. Solutions of these systems are derived using a 2D \(\mathcal Z\)-transform. The classical Cayley-Hamilton theorem is extended to 2D fractional systems described by the Roesser model. Necessary and sufficient conditions for the positivity and stabilization by the state-feedback of fractional 2D linear systems are established. A procedure for the computation of a gain matrix is proposed and illustrated by a numerical example.

MSC:

93D15 Stabilization of systems by feedback
93C55 Discrete-time control/observation systems
26A33 Fractional derivatives and integrals
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