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 cla...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.展开更多
基金US National Science Foundation (No. 1115564)North Carolina Department of Transportation (NCDOT) Research Grant (Nos. RP2013-13, RP2016-16, RP2016-19, RP2018-40)+5 种基金the Fulbright Senior Scholar Award 2016-2017, HK PolyU 2016-2017HK Branch of NRTEAETRC 2016-2017 to Prof. Sheng-Guo Wangin part by the China Scholarship Council (CSC) scholarship of 2013-2014 and Prof. Wang's NCDOT Research Grant (No. RP2013-13)Shu Liang as a co-educated Ph.D. student at the UNC Charlotte (UNCC)the Fundamental Research Funds for the China Central Universities of USTB (No. FRF-TP-17-088A1) to Shu Liangthe National Natural Science Foundation of China (No. 61873024) to Prof. Kaixiang Peng.
文摘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.
