LMI based stability condition for delta fractional order system with sector approximation

Yiheng Wei, Nan Su, Linlin Zhao and Jinde Cao

Chaos, Solitons & Fractals, 2023, vol. 174, issue C

Abstract: This paper concerns the stability of linear time invariant delay delta fractional order systems. Due to the complexity of the stable region, it is difficult or even impossible to develop a sufficient and necessary linear matrix inequality (LMI) condition. After analyzing the feature of the suggested stable region, a sector region is constructed to be the proper subset of true stable region. To control the angle of the sector region, a variable θ is introduced which improves the degree of freedom. Afterwards, the equivalent LMI condition corresponding to the sector region is developed. Notably, both the cases of α∈(0,1) and α∈(1,2) are considered. Besides the stability analysis, the developed method also be applied in controller design. Finally, the validity and efficacy of the elaborated method are illustrated by simulation study.

Keywords: Delta fractional order systems; Sector region; LMI condition; Stability analysis; Controller design (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:174:y:2023:i:c:s0960077923007178

DOI: 10.1016/j.chaos.2023.113816

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