Robust H∞ control for fractional order singular systems 0 < α < 1 with uncertainty. (30th October 2022)

• Record Type: Journal Article
• Authors: Li, Bingxin; Zhao, Xin
• Is Part Of: Optimal control applications and methods. Volume 44:Number 1(2023)
• Page Start: 332
• Page End: 348
• Publication Date: 2022-10-30
• Subjects: fractional order singular systems -- H∞$$ {H}_{\infty } $$ control -- linear matrix inequality -- robust H∞$$ {H}_{\infty } $$ control; Control theory -- Periodicals; Mathematical optimization -- Periodicals; 629.8312
• DOI: 10.1002/oca.2939
• Languages: English
• ISSNs: 0143-2087

Abstract

Abstract: This article studies robust H ∞ $$ {H}_{\infty } $$ control for fractional order singular systems (FOSS) 0 < α < 1 $$ 0<\alpha <1 $$ with uncertainty. First, the condition based on the linear matrix inequality (LMI) is obtained for fractional order systems with 0 < α < 1 $$ 0<\alpha <1 $$ in Corollary 1. Compared with existing results, by using two matrices to replace the complex matrix, the condition is easier to solve. Based on Corollary 1, the condition of H ∞ $$ {H}_{\infty } $$ control based on non‐strict LMI for FOSS without uncertainty is proposed. The strict LMI‐based conditions of H ∞ $$ {H}_{\infty } $$ control are improved to overcome the equality constraints. Finally, the LMI‐based conditions of robust H ∞ $$ {H}_{\infty } $$ control are proposed for FOSS. Four examples are shown to illustrate the effectiveness of the method.