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Fractional Calculus and Applied Analysis

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Volume 22, Issue 6


Robust stability analysis of LTI systems with fractional degree generalized frequency variables

Cuihong Wang / Yan Guo / Shiqi Zheng / YangQuan Chen
Published Online: 2019-12-31 | DOI: https://doi.org/10.1515/fca-2019-0085


A novel linear time-invariant (LTI) system model with fractional degree generalized frequency variables (FDGFVs) is proposed in this paper. This model can provide a unified form for many complex systems, including fractional-order systems, distributed-order systems, multi-agent systems and so on. This study mainly investigates the stability and robust stability problems of LTI systems with FDGFVs. By characterizing the relationship between generalized frequency variable and system matrix, a necessary and sufficient stability condition is firstly presented for such systems. Then for LTI systems with uncertain FDGFVs, we present a robust stability method in virtue of zero exclusion principle. Finally, the effectiveness of the method proposed in this paper is demonstrated by analyzing the robust stability of gene regulatory networks.

MSC 2010: Primary 26A33; Secondary 37C75; 37D20; 93D09; 93D15 93D20

Key Words and Phrases: fractional-order system; linear time-invariant systems; stability analysis; generalized frequency variables; gene regulatory networks

Dedicated to the memory of late Professor Wen Chen


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About the article

Received: 2019-07-27

Published Online: 2019-12-31

Published in Print: 2019-12-18

Citation Information: Fractional Calculus and Applied Analysis, Volume 22, Issue 6, Pages 1655–1674, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: https://doi.org/10.1515/fca-2019-0085.

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