Alternative LMI formulations for the stability of LTI fractional-order systems
1College of Sciences, Northeastern University, Shenyang, 110819, China.
Abstract:
This paper presents new linear matrix inequality (LMI) formulations for the stability analysis of fractional-order systems. Firstly, by analyzing the geometric distribution of system eigenvalues, the stability regions corresponding to different orders are characterized as unions or intersections of subregions in the complex plane. Based on this geometric interpretation, the necessary and sufficient LMI-based stability criteria are established. Secondly, to simplify the structure and improve applicability, the alternative equivalent criteria are developed, in which the power term of the system matrix is eliminated, and all LMIs rely only on real-valued matrices. Thirdly, the construction of the stability region is not unique, which leads to multiple equivalent LMI conditions and provides additional flexibility for analysis. Finally, simulation examples are presented to verify the validity and effectiveness of the proposed approach.
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