Affiliation:
1. College of Sciences, Northeastern University, Shenyang 110819, China
2. State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110819, China
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.
Funder
National Natural Science Foundation of China
Fundamental Research Funds for the Central Universities of China
Subject
Statistics and Probability,Statistical and Nonlinear Physics,Analysis