Gain‐scheduled control design for discrete‐time nonlinear systems using difference‐algebraic representations

• Published in: International journal of robust and nonlinear control Vol. 31; no. 5; pp. 1542 - 1563
• Main Authors: Reis, Gabriela L., Araújo, Rodrigo F., Torres, Leonardo A. B., Palhares, Reinaldo M.
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 25.03.2021
• Subjects: Algebra; difference‐algebraic representation; Feedback control; gain‐scheduled state feedback; input saturation; Liapunov functions; Linear matrix inequalities; local stabilization; Nonlinear systems; Optimization; parameter‐dependent Lyapunov function; Representations; State feedback
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.5362

Summary This paper addresses the local stabilization problem of nonlinear systems described by Difference‐Algebraic Representations (DAR). A novel set of sufficient Linear Matrix Inequalities (LMI) conditions are developed to design gain‐scheduled state feedback controllers. The proposed approach uses parameter‐dependent Lyapunov functions and new auxiliary decision variables aiming to obtain less conservative results. Two optimization problems are proposed to either obtain the largest estimated Domain‐of‐Attraction (DOA) or minimize the ℓ2‐gain from the energy‐bounded disturbance input to the performance output. Furthermore, this investigation considers control input saturation and system states constrained in a polyhedral region. Numerical examples are provided to illustrate the effectiveness of the proposed methodology, showing favorable comparisons with recently published similar approaches.