Analysis and description of the infinite-dimensional nature for nabla discrete fractional order systems

Fractional order systems in continuous time case are shown to be infinite-dimensional, which is an essential feature used for analysis and synthesis. The objective of this paper is to check the infinite-dimensional characteristic of nabla discrete fractional order systems. Making full use of N-transform, the actual infinite-dimensional state space model is established for both Riemann-Liouville and Caputo cases, which reveals that the finite-dimensional pseudo states are not sufficient to display the transient property of the system and only infinite-dimensional actual states are enough. Apart from these, several interesting points are discussed, including equivalent form, larger order, multiple variable and numerical implementation. (C) 2019 Elsevier B.V. All rights reserved.