Robust stability and stabilization of multi‐order fractional‐order systems with interval uncertainties: An LMI approach. (23rd February 2021)

• Record Type: Journal Article
• Authors: Lu, Jun‐Guo; Zhu, Zhen; Ma, Ying‐Dong
• Other Names: Fridman Leonid guestEditor.; Efimov Denis guestEditor.; Laghrouche Salah guestEditor.
• Is Part Of: International journal of robust and nonlinear control. Volume 31:Number 9(2021)
• Page Start: 4081
• Page End: 4099
• Publication Date: 2021-02-23
• Subjects: interval uncertainty -- linear matrix inequality -- multi‐order fractional‐order system -- robust stability -- robust stabilization; Automatic control -- Periodicals; Control theory -- Periodicals; Nonlinear systems -- Periodicals; 629.836
• DOI: 10.1002/rnc.5457
• Languages: English
• ISSNs: 1049-8923

Abstract

Abstract: This paper concentrates on the robust stability and stabilization problems of multi‐order fractional‐order systems (MOFOSs) with interval uncertainties. Firstly, the new sufficient conditions for the stability of the nominal systems are given, which are suitable for robust analysis and controller design. Then, based on the above stability conditions, the robust stability conditions for the uncertain systems are proposed. Secondly, in order to stabilize the nominal systems and uncertain systems, the state feedback controllers are designed. All the results are in the form of linear matrix inequalities and can be applied in incommensurate cases. Finally, some numerical examples are provided to verify the effectiveness of our results.