Deterministic analysis of distributed order systems using operational matrix

• Published in: Applied mathematical modelling Vol. 40; no. 3; pp. 1929 - 1940
• Main Authors: Duong, Pham Luu Trung, Kwok, Ezra, Lee, Moonyong
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01-02-2016
• Subjects: Block pulse function; Distributed order system; Fractional differential equation; Operational matrix; Fractional differential equation; Operational matrix; Distributed order system; Block pulse function
• ISSN: 0307-904X
• DOI: 10.1016/j.apm.2015.09.035

•Novel approach using operation matrix for deterministic analysis of linear distributed order systems.•Reduce different analysis problems by using block pulse functions.•Address arbitrary input without knowledge of Laplace transform.•Accurate and efficient for deterministic analysis.
Recently, distributed order systems as a generalized concept of fractional order have been a major focus in science and engineering areas, and have rapidly extended application across a wide range of disciplines. However, only a few numerical methods are available for analyzing the distributed order systems. This paper proposes a novel numerical scheme to analyze the behavior of single input single output linear systems in the time domain with a single distributed order differentiator/integrator by using operational matrix technique. The proposed method reduces different analysis problems to a system of algebraic equations by using block pulse functions, which makes it easy to handle an arbitrary input. Numerical examples were used to illustrate the accuracy and computational efficiency of the proposed method. The proposed method was found to be an efficient tool for analyzing linear distributed order systems.