Reduced-order Nonlinear Observer Design for Two-time-scale Systems

A two-time-scale system involves both fast and slow dynamics. This paper studies the design of nonlinear observers for general nonlinear two-time-scale systems and presents a reduced-order observer design approach. The reduced-order observer is derived based on a lower dimensional model to reconstruct the slow states, along with the algebraic slow-motion invariant manifold function to reconstruct the fast states. Through an error analysis, it is shown that even though the observer is designed based on the reduced model by neglecting the fast dynamics, it is capable of providing accurate estimation of the states of the original detailed system. It will render a vanishing estimation error, with exponential convergence rate governed by the subsystem of fast dynamics and the chosen observer design parameters.