Dynamic gain observer design for Lipschitz nonlinear systems subjected to noise

The problem of designing an observer for nonlinear Lipschitz systems affected by system and sensor noises is addressed. Related to the system nonlinearity, the stability of observer dynamic with static and dynamic gain is considered. The advantage of using dynamic gain to deal with large Lipschitz nonlinearity is discussed and it is proved that no dynamic gain can stabilise the observer for a larger Lipschitz constant as compared with the static gain. However, a nonlinear observer with dynamic gain has some additional degrees of freedom which can be utilised to attenuate noise effect on the observer behaviour. Using mixed and criteria, this article introduces a method to obtain a dynamic gain which can deal with system nonlinearity and noise simultaneously. The effectiveness of the proposed method is finally demonstrated by some simulation results.