Feedback stabilisation control design for fractional order non‐linear systems in the lower triangular form. Issue 9 (1st June 2016)

• Record Type: Journal Article
• Authors: Zhao, Yige; Wang, Yuzhen; Zhang, Xianfu; Li, Haitao
• Is Part Of: IET control theory & applications. Volume 10:Issue 9(2016)
• Page Start: 1061
• Page End: 1068
• Publication Date: 2016-06-01
• Subjects: state feedback -- closed loop systems -- nonlinear systems -- Lyapunov methods -- control system synthesis -- matrix algebra -- asymptotic stability; fractional order nonlinear systems -- lower triangular form -- Lyapunov function method -- output feedback stabilisation control design problems -- Caputo fractional derivative -- feedback stabiliser design problem -- Lyapunov equation -- relevant matrix inequalities -- state feedback stabilisers -- output feedback stabilisers -- closed loop system -- asymptotic stability; Control theory -- Periodicals; Automatic control -- Periodicals; 629.8312
• DOI: 10.1049/iet-cta.2015.0130
• Languages: English
• ISSNs: 1751-8644

Abstract

Abstract : Using the Lyapunov function method, this study investigates both state and output feedback stabilisation control design problems for fractional order non‐linear systems in the lower triangular form, and presents a number of new results. First, some new properties for Caputo fractional derivative are presented. Second, by introducing appropriate transformations of coordinates, the feedback stabiliser design problem is converted into the determination of finding some parameters, which can be obtained by solving the Lyapunov equation and relevant matrix inequalities. Finally, based on the Lyapunov function method, both state and output feedback stabilisers are explicitly designed to make the closed‐loop system asymptotically stable. The study of an illustrative example shows that the obtained results are effective in designing feedback stabilisers for fractional order non‐linear systems in the lower triangular form.