Robust observer design for uncertain one-sided Lipschitz systems with disturbances

In this paper, we study the robust observer design problem for a class of uncertain one-sided Lipschitz systems with disturbances. Not only the system matrices but also the nonlinear functions are assumed to be uncertain. The nominal models of nonlinearities are assumed to satisfy both the one-sided Lipschitz condition and the quadratically inner-bounded condition. By utilizing a novel approach, our observer designs are robust against unknown nonlinear uncertainties and system and measurement noises. The new approach also relaxes some conservativeness in related existing results, ie, less conservative observer design conditions are obtained. Furthermore, the problem of designing reduced-order observers is considered in case the output measurement is not subject to uncertainty and disturbance. Two examples are provided to show the efficiency and advantages of our results over existing works.