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Robust Stability Analysis of Uncertain Linear Fractional-Order Systems with Time-Varying Uncertainty For 0<a<2

[+] Author and Article Information
Mohammad Tavazoei

School of Electrical and Computer Engineering, Shiraz University, Shiraz, Iran
mtavazoei23@gmail.com

Mohammad Hassan Asemani

School of Electrical and Computer Engineering, Shiraz University, Shiraz, Iran
asemani@shirazu.ac.ir

1Corresponding author.

ASME doi:10.1115/1.4041607 History: Received September 14, 2018; Revised September 26, 2018

Abstract

This paper focuses on the stability analysis of the linear fractional-order systems with fractional order 0<a<2, in presence of time-varying uncertainty. To obtain a robust stability condition, we first derive a new upper bound for the norm of Mittag-Leffler function associated with the nominal fractional-order system matrix. Then, by finding an upper bound for the norm of the uncertain fractional-order system solution, a sufficient non-Lyapunov robust stability condition is proposed. Unlike the previous methods for robust stability analysis of uncertain fractional-order systems, the proposed stability condition is applicable to systems with time-varying uncertainty. Moreover, the proposed condition depends on the fractional order of the system and the upper bound of the uncertainty matrix norm. Finally, the offered stability criteria are examined on a numerical uncertain linear fractional-order systems with and to verify the applicability of the proposed conditions. Furthermore, the stability of an uncertain fractional-order Sallen-Key filter is checked via the offered conditions.

Copyright (c) 2018 by ASME
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