Admissibility and robust stabilization of continuous linear singular fractional order systems with the fractional order α: The 0<α<1 case

Xuefeng Zhang; YangQuan Chen

doi:10.1016/j.isatra.2017.03.008

Admissibility and robust stabilization of continuous linear singular fractional order systems with the fractional order α: The 0<α<1 case

ISA Trans. 2018 Nov:82:42-50. doi: 10.1016/j.isatra.2017.03.008. Epub 2017 Apr 4.

Authors

Xuefeng Zhang¹, YangQuan Chen²

Affiliations

¹ School of Sciences, Northeastern University, Shenyang, Liaoning 110004, China. Electronic address: zhangxuefeng@mail.neu.edu.cn.
² Embedded Systems and Automation Lab School of Engineering, University of California, Merced, CA 95343, USA. Electronic address: ychen53@ucmerced.edu.

PMID: 28385193
DOI: 10.1016/j.isatra.2017.03.008

Abstract

This paper presents three different necessary and sufficient conditions for the admissibility and robust stabilization of singular fractional order systems (FOS) with the fractional order α:0<α<1 case. Two results are obtained in terms of strict linear matrix inequalities (LMIs) without equality constraint. The system uncertainties considered are norm bounded instead of interval uncertainties. The equivalence between quadratic admissibility and general quadric stability for FOS are derived. A condition is not only strict LMI condition without quality constraint but also avoid a singularity trouble caused by the superfluous solved variable. When α=1 and E=I, the three results reduce to the conditions of stability and robust stabilization of normal integer order systems. Numerical examples are given to verify the effectiveness of the criteria. With the approaches proposed in this technical note, we can analyze and design singular fractional order systems with similar way to the normal integer order systems.

Keywords: Admissibility; Fractional order systems; Linear matrix inequalities; Singular systems; Stabilization.