Alternative criteria for admissibility and stabilization of singular fractional order systems

Xuefeng Zhang; Zhe Wang

doi:10.3934/mfc.2019017

Article Contents

2019, Volume 2, Issue 3: 267-277. Doi: 10.3934/mfc.2019017

This issue Previous Article Eigenstructure assignment for polynomial matrix systems ensuring normalization and impulse elimination Next Article

Alternative criteria for admissibility and stabilization of singular fractional order systems

Xuefeng Zhang^, and
Zhe Wang

School of Sciences, Northeastern University, No. 3 Wenhua Road Heping District, Shengyang 110819, Liaoning, China

^* Corresponding author: Xuefeng Zhang
^* Corresponding author: Xuefeng Zhang

Received: June 2019

Revised: August 2019

Published: September 2019

The first author is supported by NSFC 61603055.

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Abstract

This paper discusses admissibility problem of singular fractional order systems with order $ 1<\alpha<2 $. The alternative necessary and sufficient admissibility conditions are proposed, in which include linear matrix inequalities (LMIs) with equality constraints and LMIs without equality constraints. Moreover, these criteria are brand-new and different from the existing results. The state feedback control to stabilize singular fractional order systems is derived. Two numerical examples are presented to shown the effectiveness of our results.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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Figure 1. The closed-loop fractional order system in Example 2

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