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Routh table test for stability of commensurate fractional degree polynomials and their commensurate fractional order systems

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Abstract

A Routh table test for stability of commensurate fractional degree polynomials and their commensurate fractional order systems is presented via an auxiliary integer degree polynomial. The presented Routh test is a classical Routh table test on the auxiliary integer degree polynomial derived from and for the commensurate fractional degree polynomial. The theoretical proof of this proposed approach is provided by utilizing Argument principle and Cauchy index. Illustrative examples show efficiency of the presented approach for stability test of commensurate fractional degree polynomials and commensurate fractional order systems. So far, only one Routh-type test approach [1] is available for the commensurate fractional degree polynomials in the literature. Thus, this classical Routh-type test approach and the one in [1] both can be applied to stability analysis and design for the fractional order systems, while the one presented in this paper is easy for peoples, who are familiar with the classical Routh table test, to use.

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Acknowledgements

Prof. Sheng-Guo Wang expresses his appreciation to Prof. Yong Wang at the University of Science and Technology of China for his cooperation during 2013–2016 since his Ph.D. student visited UNCC as a co-educated Ph.D. student.

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Authors and Affiliations

  1. College of Engineering and College of Computing and Informatics, University of North Carolina at Charlotte, Charlotte, NC, 28223-0001, USA

    Sheng-Guo Wang

  2. School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing, 100083, China

    Shu Liang, Liang Ma & Kaixiang Peng

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  1. Sheng-Guo Wang
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  2. Shu Liang
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Correspondence to Sheng-Guo Wang.

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This work was supported in part by the US National Science Foundation (No. 1115564), North Carolina Department of Transportation (NCDOT) Research Grant (Nos. RP2013-13, RP2016-16, RP2016-19, RP2018-40), the Fulbright Senior Scholar Award 2016–2017, HK PolyU 2016–2017, and HK Branch of NRTEAETRC 2016–2017 to Prof. Sheng-Guo Wang; in part by the China Scholarship Council (CSC) scholarship of 2013–2014 and Prof. Wang’s NCDOT Research Grant (No. RP2013-13) to Shu Liang as a co-educated Ph.D. student at the UNC Charlotte (UNCC), and the Fundamental Research Funds for the China Central Universities of USTB (No. FRF-TP-17-088A1) to Shu Liang; and the National Natural Science Foundation of China (No. 61873024) to Prof. Kaixiang Peng. This work was mainly done at the UNCC.

Liang MA received the B.E. degree in Automation and the M.E. degree in Control Theory and Control Engineering from North China University of Science and Technology, Tangshan, China, in 2009 and 2012, respectively. He is currently working toward the Ph.D. degree at the School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing, China. His research interest focuses on process monitoring and fault diagnosis for process industries.

Kaixiang PENG received his B.Sc., M.Sc., and Ph.D. degrees from University of Science and Technology Beijing, in 1995, 2002, and 2007, respectively. He is currently a Professor in the School of Automation and Electrical Engineering, University of Science and Technology Beijing. From January to July in 2012, he visited University of Duisburg-Essen as a visiting scholar in the institute of Automatic Control and Complex Systems. His research interest covers statistical process monitoring and fault diagnosis, process modeling and control for the iron and steel industry.

Sheng-Guo WANG received his B.Sc. and M.Sc. degrees in EE from University of Science and Technology of China in Beijing 1967 and Hefei 1981, respectively, and Ph.D. in ECE from University of Houston in 1994. His major is automatic control and systems with a minor in computer science. He is currently a professor at University of North Carolina at Charlotte. He has published more than 100 refereed papers. He has been the PI for numerous various research projects since 1974. He has served as Associate Editor for several journals, and Program Committee Member (more than 20 times) and Session Chair (more than 10 times) for international conferences. He has been a reviewer for more than 30 journals. Prof. Wang is a recipient of many academic awards, including 1978 China National Science Conference Award (one of the highest academic honor in China), US Fulbright Senior Scholar Award as Fulbright-PolyU Senior Scholar in HK 2016–2017 (the flagship international educational exchange program in the world), British Council Scholar 1989–1990, Sigma Xi Research Excellence Award (UH Chapter) 1994, Outstanding Faculty PVAMU 1997, and Inventor for UNC Charlotte Invention 2001. Recently, his research project has made valued contributions, received the 2015 US “Sweet 16” High Value Research Project Award, as “Makes the Difference 2015, Innovation Advances Transportation–A Green Transportation System–Automation Provides Faster Wetlands Assessment in North Carolina” issued by the US AASTHO & RAC.

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Wang, SG., Liang, S., Ma, L. et al. Routh table test for stability of commensurate fractional degree polynomials and their commensurate fractional order systems. Control Theory Technol. 17, 297–306 (2019). https://doi.org/10.1007/s11768-019-8127-4

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  • DOI: https://doi.org/10.1007/s11768-019-8127-4

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