Design of robust nonfragile H∞ controller for uncertain nonlinear polynomial systems

• Published in: Optimal control applications & methods Vol. 40; no. 1; pp. 55 - 67
• Main Authors: Rezgui, Marwa, Ayadi, Hela Belkhiria, Benhadj Braiek, Naceur
• Format: Journal Article
• Language: English
• Published: Glasgow Wiley Subscription Services, Inc 01-01-2019
• Subjects: Attenuation; Control stability; Control systems design; Controllers; H-infinity control; H∞ control; Kronecker product; linear matrix inequalities; Mathematical analysis; Matrix methods; nonfragile controller; Nonlinear control; nonlinear polynomial systems; Nonlinear systems; Polynomials; Robust control; Uncertainty
• ISSN: 0143-2087; 1099-1514
• DOI: 10.1002/oca.2466

Summary
This paper is concerned with the robust H∞ nonfragile controller design for a particular class of nonlinear systems, namely, the perturbed polynomial systems, which are subject to unstructured bounded uncertainties in both the system model and the control law. Combining the Lyapunov stability theory, properties of linear matrix inequality, and Kronecker product properties, a sufficient condition of robust H∞ nonfragile control design is proposed. More specifically, we propose a robust H∞ controller of nonlinear polynomial systems with additive unstructured uncertainties and variation in the control law itself that guarantee the stability and the attenuation of external perturbations. Two examples are provided to illustrate the effectiveness of the proposed approach.