One-sided Lipschitz observer design for circadian models

This paper deals with observer designs to mathematical models of circadian rhythms which exist in every living organism. Two mathematical models are considered, with a 3rd order model for Neurospora, and a 7th order model for Mammals. The observer design is based on systems with Lipschitz nonlinearities. In particular, observers based on onesided Lipschitz condition are investigated, and the observers are then designed for both circadian models. Detailed analysis is performed for nonlinear functions in the models to show the one-sided Lipschitz observers can indeed be applied. Several simulations studies of proposed observers are carried out with the results shown in this paper.