Mittag-leffler string stability of singularly perturbed stochastic systems within local fractal space

Abstract

In this paper, we define a new type of string stability based on Mittag-Leffler function so-called Mittag-Leffler (p\alpha)-string stability. This kind of stability for a class of singularly perturbed stochastic systems of fractional order will be considered. The fractional derivative in these systems is in the local sense. String stability indicates uniform boundedness of the interconnected system if the initial cases of interconnected system be uniformly bounded. The deduction of the sufficient conditions of stability is based on a mixture of the concept of the Mittag-Leffler stability with the notion of p-mean string stability of singularly perturbed stochastic systems. In the sequel, our purpose is to investigate the full order system in their lower order subsystems, i.e., the reduced order system and the boundary layer correction.