Positive 2D fractional linear systems

Abstract

Purpose

The purpose of this paper is to introduce a new class of positive two‐dimensional (2D) fractional linear systems.

Design/methodology/approach

A notion (concept) of order 2D difference is proposed and the solution to the state equations is given.

Findings

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.

Originality/value

A method for analysis of positive 2D fractional linear systems is proposed.

Citation

Kaczorek, T. (2009), "Positive 2D fractional linear systems", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 28 No. 2, pp. 341-352. https://doi.org/10.1108/03321640910929254