High gain observer design for a class of MIMO non uniformly observable uncertain systems

A high gain observer is proposed for a class of MIMO non uniformly observable systems including uncertainties. The gain of the proposed observer is issued from the resolution of a Lyapunov differential equation and its tuning can be achieved through the choice of a single scalar parameter. The observer design is made under an appropriate set of conditions given in terms of appropriate excitation. It is shown that in the absence of uncertainties, the observation error converges exponentially to zero. In the case where the uncertainties are bounded, this error can be made as small as desired by choosing high values of the observer design parameter. Simulation results are given for illustration purposes.