Reachability of positive 2D fractional linear systems

Two new classes of positive two-dimensional (2D) fractional linear systems are introduced in this work. Two definitions of fractional differences of 2D function are proposed. The solutions of fractional 2D state equations of the linear systems are given. The classical Cayley–Hamilton theorem is extended to 2D fractional systems. The necessary and sufficient conditions for the positivity of 2D fractional systems are established. The notion of reachability is introduced for the positive fractional systems and the necessary and sufficient conditions for the reachability are established. The considerations are illustrated with numerical examples.

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