Generalized Criteria for Admissibility of Singular Fractional Order Systems

Abstract

Unified frameworks for fractional order systems with fractional order 0<α<2 are worth investigating. The aim of this paper is to provide a unified framework for stability and admissibility for fractional order systems and singular fractional order systems with 0<α<2, respectively. By virtue of the LMI region and GLMI region, five stability theorems are presented. Two admissibility theorems for singular fractional order systems are extended from Theorem 5, and, in particular, a strict LMI stability criterion involving the least real decision variables without equality constraint by isomorphic mapping and congruent transform. The equivalence between the admissibility Theorems 6 and 7 is derived. The proposed framework contains some other existing results in the case of 1≤α<2 or 0<α<1. Compared with published unified frameworks, the proposed framework is truly unified and does not require additional conditional assignment. Finally, without loss of generality, a unified control law is designed to make the singular feedback system admissible based on the criterion in a strict LMI framework and demonstrated by two numerical examples.