Stabilization of nonlinear time-delay systems with input saturation via anti-windup fuzzy design

• Published in: Soft computing (Berlin, Germany) Vol. 15; no. 5; pp. 877 - 888
• Main Authors: Ting, Chen-Sheng, Liu, Chuan-Sheng
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.05.2011; Springer Nature B.V
• Subjects: Artificial Intelligence; Closed loops; Computational Intelligence; Control; Control algorithms; Controllers; Convexity; Design; Design analysis; Engineering; Feedback control; Focus; Fuzzy control; Fuzzy sets; Linear matrix inequalities; Mathematical analysis; Mathematical Logic and Foundations; Mechatronics; Nonlinear control; Nonlinear systems; Nonlinearity; Robotics; Stability analysis; Time delay systems; Linear matrix inequality; T–S fuzzy model; Domain of attraction; Anti-windup fuzzy controller
• ISSN: 1432-7643; 1433-7479
• DOI: 10.1007/s00500-010-0555-5

This investigation considers stability analysis and control design for nonlinear time-delay systems subject to input saturation. An anti-windup fuzzy control approach, based on fuzzy modeling of nonlinear systems, is developed to deal with the problems of stabilization of the closed-loop system and enlargement of the domain of attraction. To facilitate the designing work, the nonlinearity of saturation is first characterized by sector conditions, which provide a basis for analysis and synthesis of the anti-windup fuzzy control scheme. Then, the Lyapunov–Krasovskii delay-independent and delay-dependent functional approaches are applied to establish sufficient conditions that ensure convergence of all admissible initial states within the domain of attraction. These conditions are formulated as a convex optimization problem with constraints provided by a set of linear matrix inequalities. Finally, numeric examples are given to validate the proposed method.