Positivity and stabilization of fractional 2D linear systems described by the Roesser model

Authors:
Tadeusz Kaczorek;Krzysztof Rogowski
Affiliations:
Faculty of Electical Engineering, Białystok Technical University, Wiejska 45D, 15-351 Białystok, Poland;Faculty of Electical Engineering, Białystok Technical University, Wiejska 45D, 15-351 Białystok, Poland
Venue:
International Journal of Applied Mathematics and Computer Science - Computational Intelligence in Modern Control Systems
Year:
2010

Citing 2
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Abstract

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 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.