Reduced-order observer design for one-sided Lipschitz time-delay systems subject to unknown inputs

• Published in: IET control theory & applications Vol. 10; no. 10; pp. 1097 - 1105
• Main Authors: Cuong Nguyen, Minh, Trinh, Hieu
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 27.06.2016
• Subjects: asymptotic observer design; Asymptotic properties; control nonlinearities; control system synthesis; delays; Design engineering; Disturbances; Dynamical systems; H∞ control; H∞ observer design; Inequalities; Jensen inequality; linear matrix inequalities; nonlinear control systems; nonlinear observer design problem; nonlinear systems; Nonlinearity; observers; one‐sided Lipschitz time‐delay systems; quadratically inner‐bounded condition; reduced order systems; reduced‐order observer design; Regular Papers; Synthesis; synthesis conditions; system disturbances; Time delay; unknown inputs; Wirtinger‐based integral inequality; control system synthesis; quadratically inner-bounded condition; Jensen inequality; nonlinear observer design problem; one-sided Lipschitz time-delay systems; asymptotic observer design; unknown inputs; nonlinear systems; H∞ observer design; H∞ control; linear matrix inequalities; delays; nonlinear control systems; control nonlinearities; Wirtinger-based integral inequality; reduced order systems; synthesis conditions; system disturbances; reduced-order observer design; observers
• ISSN: 1751-8644; 1751-8652
• DOI: 10.1049/iet-cta.2015.1173

This study addresses the observer design problem for a class of one-sided Lipschitz time-delay systems in the presence of unknown inputs. The non-linearities are assumed to satisfy the one-sided Lipschitz and quadratically inner-bounded conditions; hence, a wider class of non-linear systems is investigated in this work. A novel approach for the non-linear observer design problem subject to time delays and disturbances is proposed. Both H∞ observer design and asymptotic observer design with reduced-order are introduced. To deal with the time-delay issue, Wirtinger-based integral inequality, which encompasses the Jensen inequality, is employed to derive less conservative synthesis conditions in linear matrix inequalities form. Two numerical examples are given to illustrate the effectiveness and the edge of the authors' results over other relevant works in the literature.