Generalized Multiple Delay-dependent H∞, Functional Observer Design for Nonlinear System

• Published in: International journal of control, automation, and systems Vol. 21; no. 11; pp. 3584 - 3594
• Main Authors: Naami, Ghali, Ouahi, Mohamed, Alvarez, Teresa, Rabhi, Abdelhamid
• Format: Journal Article
• Language: English
• Published: Bucheon / Seoul Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers 01.11.2023; Springer Nature B.V; Springer
• Subjects: Control; Engineering; Engineering Sciences; H infinity; Liapunov functions; Mechatronics; Nonlinear systems; Nonlinearity; Observers; Optimization; Regular Papers; Robotics; nonlinear systems; Lyapunov functions; time delays; functional observers; linear matrix inequalities (LMIs); Disturbances
• ISSN: 1598-6446; 2005-4092
• DOI: 10.1007/s12555-023-0087-2

Functional observers are the major alternative to many practical estimation problems where full-order observers cannot be used. This paper introduces a generalized approach to design H ∞ functional observers for a class of Lipschitz nonlinear systems with multiple time delays. Moreover, the considered system extends from previously published work in that it presents nonlinearity, multiple delay and external disturbance. Their main findings come from the development of a generalized augmented Lyapunov function that uses both the extended reciprocal convex combination and the Wirtinger inequality. The stability of the observer is therefore guaranteed by an LMI optimization problem. Finally, the steps of the design procedure were condensed and proffered for the two numerical examples to test the recommended design approach.