Design of observer for one-sided Lipschitz nonlinear systems with interval time-varying delay

This paper deals with state observer design problem for a class of nonlinear dynamical systems with interval time-varying delay that satisfies the one-sided Lipschitz condition. The systems under consideration include the well-studied Lipschitz system as a special case and possess inherent advantages with respect to conservativeness. By constructing a novel Lyapunov-Krasovskii functional and utilizing free-weighting matrices approach, novel sufficient conditions that guarantee the observer error converge asymptotically to zero are obtained for a class of nonlinear dynamical systems with interval time-varying delay in terms of linear matrix inequalities. The computing method for observer gain matrix is given. Finally, illustrative examples are given to demonstrate the effectiveness of the proposed method. Key-Words: Nonlinear observers; One-sided Lipschitz condition; Quadratic inner-boundedness; Asymptotic stability; Interval time-varying delay