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

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.