Robust stability and stabilization of multi‐order fractional‐order systems with interval uncertainties: An LMI approach

• Published in: International journal of robust and nonlinear control Vol. 31; no. 9; pp. 4081 - 4099
• Main Authors: Lu, Jun‐Guo, Zhu, Zhen, Ma, Ying‐Dong
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 01.06.2021
• Subjects: Control stability; Control systems design; Feedback control; interval uncertainty; Linear matrix inequalities; linear matrix inequality; Mathematical analysis; multi‐order fractional‐order system; Robust control; robust stability; robust stabilization; Stability analysis; State feedback; Uncertainty
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.5457

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.