A simple filtered high gain observer for a class of uncertain nonlinear systems

A high gain observer involving a linear filter is proposed. The structure of the proposed Filtered High Gain Observer (FHGO) is very simple and consists in two cascaded systems having the same dimension as the original system. The first subsystem is a copy of the original system with a simple correction term which only (linearly) depends on the state of the second subsystem. The latter is a linear filter which input is the output observation error, i.e. the error between the output measurement and its value predicted by the first subsystem. The design of the FHGO is first carried out by assuming that the outputs are available in a continuous manner. Then, a redesigned version is proposed in order to account for the sampling process of the output. Simulation results dealing with a forced Van Der Pol oscillator are given for illustration purposes.