Design of unknown input observer for nonlinear systems with time-varying delays

A method of designing unknown input observer (UIO) for a class of nonlinear systems with time-varying delays is presented. The observer is designed using linear matrix inequality approach for the nonlinear systems whose nonlinear state update function satisfies Lipschitz condition. It is also assumed that the unknown inputs can be decoupled from nonlinear function when these appear in the function. Two types of time-delay scenarios have been considered for designing the observers. First an UIO is designed considering state time-delays only in the linear part of the system. Then the idea is expanded for designing the observer for more general kind of time-delay setup where the time-delays arise in both linear and nonlinear parts of the system. Sufficient conditions for the existence of these observers are also derived. The effectiveness of the proposed observer is shown with numerical results, which confirm that it estimates the states quite precisely for nonlinear time-delay systems. © 2014, Springer-Verlag Berlin Heidelberg.