Reduced-order observer design of multi-output nonlinear systems with application to a circadian model

In this paper we present a new design of reduced-order observers which can be applied to a class of multi-output nonlinear systems. In this new method, the observer error dynamics can be designed by choosing the observer gain, unlike the existing method in literature, of which the observer error dynamics depend on the invariant zeros. Observer design of a fourth-order nonlinear system is used to demonstrate the proposed design procedure, before the application to the seventh-order mathematical model of circadian rhythms. The results of the observer design for the circadian model are useful to the people who are working on circadian rhythms for the possible reduction in the measurements. Several simulation studies of the proposed observer design are carried out with the results shown in this paper.