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

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.