The full order robust unknown input observers for continuous systems are presented. The observers are designed for both linear and nonlinear systems considering both noise and uncertainties. First, an unknown input observer is designed for linear systems. The observer is derived based on linear matrix inequality (LMI) approach. Then the observer design problem is extended for a class of nonlinear systems whose nonlinear function satisfies the Lipschitz condition. The main advantage of these observers over the existing works on UIO design is that these can handle both noise and uncertainties simultaneously. The performance of the observers is demonstrated by applying it to the robust state estimation of single link robot arm.