Novel stability results of multivariable fractional-order system with time delay

Zhe Zhang, Yaonan Wang, Jing Zhang, Zhaoyang Ai and Feng Liu

Chaos, Solitons & Fractals, 2022, vol. 157, issue C

Abstract: This paper deduces some novel asymptotic stability criteria for different forms of multivariable fractional-order systems (MFOS) whose fractional-order parameters are between 0 and 1 with time delays based on M-matrix. First, we extend the general asymptotic stability condition of ordinary systems to MFOS. Then, we investigate into the linear and nonlinear MFOS, then the asymptotic stability criterion of which derived based on M-matrix. Then, for the asymptotically stability study of the relatively complex MFOS with time delay, we also present the asymptotic stability criterion via the new method. In addition, we conduct an in-depth discussion on the stability of MFOS and integer order multivariable systems, and intuitively show the advantages of fractional-order systems through time responses. Compared with the fractional-order comparison principle, the new asymptotic stability criteria have the advantages of fewer restrictions, less conservativeness, and a wider applicability. Finally, four examples which contain MFOS covering different categories are shown.

Keywords: Fractional-order systems; Asymptotic stability; Multivariable systems; Time delay (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:157:y:2022:i:c:s0960077922001539

DOI: 10.1016/j.chaos.2022.111943

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