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Robust Stability Analysis of Distributed-Order LTI Systems with Uncertain Order Weight Functions and Uncertain Dynamic Matrices

[+] Author and Article Information
Mohammad Saleh Tavazoei

Electrical Engineering Department, Sharif University of Technology, Tehran, Iran
tavazoei@sharif.edu

Hamed Taghavian

Electrical Engineering Department, Sharif University of Technology, Tehran, Iran
hamed.taghavian@gmail.com

1Corresponding author.

ASME doi:10.1115/1.4037268 History: Received June 27, 2016; Revised June 12, 2017

Abstract

BIBO stability of distributed-order LTI systems with uncertain order weight functions and uncertain dynamic matrices is investigated in this paper. The order weight function in these uncertain systems is assumed to be totally unknown lying between two known positive bounds. First, some properties of stability boundaries of fractional distributed-order systems with respect to location of eigenvalues of dynamic matrix are proved. Then, on the basis of these properties it is shown that the stability boundary of distributed-order systems with the aforementioned uncertain order weight functions is located in a certain region on the complex plane defined by the upper and lower bounds of the order weight function. Thereby, sufficient conditions are obtained to ensure robust stability in distributed-order LTI systems with uncertain order weight functions and uncertain dynamic matrices. Numerical examples are presented to verify the obtained results.

Copyright (c) 2017 by ASME
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