H∞ finite-time bounded observer design for nonlinear systems with time-delay

A H-infinity finite-time bounded observer for quasi-one-sided Lipschitz nonlinear systems with time-delay is considered in this paper. First, the form of observer is designed and error dynamics is obtained. Using a class of Lyapunov Krasovskii functional, new sufficient conditions of stabilizing this kind of error systems are drawn. Secondly, nonlinear matrix inequalities are transformed into linear matrix inequalities by restraining the eigenvalues of positive definite matrices of both delayed and non-delayed states. Then the finite-time bounded observer is obtained such that the error dynamics is finite-time bounded and satisfies a given H-infinity bounded condition. Finally, a simple pendulum motion model is given to illustrate the effectiveness of the proposed method.