Title: Discrete state space systems of fractional order

Authors: Jagan Mohan Jonnalagadda

Addresses: Department of Mathematics, Birla Institute of Technology and Science Pilani, Hyderabad 500 078, Telangana, India

Abstract: The present article devotes to the study of linear time invariant discrete fractional order state space systems using a novel approach. First, we replace the conventional Grünwald-Letnikov-type backward difference operator with the equivalent Riemann-Liouville-type nabla difference operator and obtain the system response using variation of constants and discrete Laplace transform methods. Next, we present three different algorithms to construct state transition matrix of the system. Finally, we provide an example to illustrate the applicability of established result.

Keywords: backward (nabla) difference; fractional order; matrix exponential function; N-transform; state space representation; state transition matrix; system response.

DOI: 10.1504/IJDSDE.2018.092676

International Journal of Dynamical Systems and Differential Equations, 2018 Vol.8 No.3, pp.228 - 241

Received: 23 Mar 2017
Accepted: 02 Aug 2017

Published online: 27 Jun 2018 *

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