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

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