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Routh table test for stability of commensurate fractional degree polynomials and their commensurate fractional order systems
Sheng-GuoWANG,ShuLIANG,LiangMA,KaixiangPENG
0
(University of North Carolina at Charlotte, USA)
摘要:
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.
关键词:  Fractional order systems, stability, commensurate fractional degree polynomials, Routh table test
DOI:
基金项目: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.
Routh table test for stability of commensurate fractional degree polynomials and their commensurate fractional order systems
Sheng-Guo WANG,Shu LIANG,Liang MA,Kaixiang PENG
(College of Engineering and College of Computing and Informatics, University of North Carolina at Charlotte, NC 28223-0001, U.S.A.;School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China)
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.
Key words:  Fractional order systems, stability, commensurate fractional degree polynomials, Routh table test