Observer Design For Several Nonlinear Time - Varying Systems With Time - Varying Delays

The problems of observer and controller design for nonlinear systems with time-varying delay are important subjects in the field of nonlinear systems. In the dissertation, the stability analysis as well as observer and controller design for several classes of nonlinear systems with time-varying delay are investigated. The main contributions of this dissertation are given as follows:Firstly, 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. For given observer gain L, 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. For unknown observer gain L, novel sufficient conditions that guarantee the observer error converge asymptotically to zero are established for a class of nonlinear dynamical systems with interval time-varying delay. The computing method for observer gain matrix is given. Furthermore, novel sufficient conditions that guarantee the observer error converge asymptotically to zero are obtained for a class of linear dynamical systems with interval time-varying delay. And the computing method for observer gain matrix is given. At last, illustrative examples are given to demonstrate the effectiveness of the proposed method.Secondly, this paper investigates the problem of state observer design for a class of nonlinear dynamical systems with interval time-varying delay and uncertainties that satisfies the one-sided Lipschitz condition. For given observer gain L, based on 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. For unknown observer gain L, novel sufficient conditions that guarantee the observer error converge asymptotically to zero are proposed for a class of nonlinear dynamical systems with interval time-varying delay. The computing method for observer gain matrix is given. Moreover, novel sufficient conditions that guarantee the observer error converge asymptotically to zero are obtained for a class of nonlinear dynamical systems with often delay. And the computing method for observer gain matrix is given. At last, illustrative examples are given to demonstrate the effectiveness of the proposed method.Finally, this paper investigates the problems of finite-time boundedness and observer-based H∞ finite-time stabilization for a class of switched neutral systems with mixed time-varying delays and nonlinear perturbation. Based on novel Lyapunov-Krasovskii functional and utilizing free-weighting matrices approach and average dwell time technique, novel sufficient conditions that guarantee the nonlinear switched neutral system is finite-time bounded are established in terms of linear matrix inequalities. Then, by constructing Lyapunov-Krasovskii functional and utilizing free-weighting matrices approach and average dwell time technique, novel criteria that guarantee the nonlinear switched neutral systems are observer-based output feedback finite-time stabilizable are proposed in terms of linear matrix inequalities. The computing method for controller gain matrices and observer gain matrix are given. Furthermore, novel sufficient conditions that guarantee the nonlinear switched neutral systems are observer-based H∞ finite-time stabilizable are given. At last, illustrative examples are given to demonstrate the effectiveness of the proposed method.