Functional Observer And Tracking Control Design For One-Sided Lipschitz Nonlinear Systems With Time-delay

In recent twenty years, the observer design and tracking control for nonlinear systems have attracted considerable attention, and many design methods are proposed. Based on Lyapunov-Krasovskii functional and linear matrix inequality (LMI) theory, this paper investigated the function observer and tracking control design for one-sided Lipschitz nonlinear system with time-delay. The main contents are as follows:Firstly, the functional observer design for one-sided Lipschitz nonlinear systems with time-delay is studied. Based on linear matrix inequality (LMI) theory, sufficient conditions of existence for gain matrices are given by choosing a suitable Lyapunov-Krasovskii functional. A systematic design method is presented for the gain matrices of functional observer. An example is provided to verify the effectiveness of the functional observer design.Secondly, the H∞ functional observer design for one-sided Lipschitz nonlinear systems with time-delay is studied. Aiming at the one-sided Lipschitz nonlinear systems with time-delay, existence conditions and expressions for gain matrices of the observer are acquired by using the generalized inverse method. Making full use of the one-sided Lipschitz condition and quadratic inner-bounded condition, gain matrices are further determined based on the linear matrix inequality theory. The stability of the error dynamic system is proved by selecting a suitable Lyapunov-Krasovskii functional. For such systems in the absence of noises, the error dynamics asymptotically converge to zero. For such systems in the presence of noises, the proposed functional observer can effectively suppress disturbances. In order to illustrate the effectiveness of the proposed observer design, Simulation example illustrates the effectiveness of the proposed obsever design through the comparisons of functional observer design which under the condition of time-delay and non-time-delayFinally, the problem of tracking control for one-sided Lipschitz nonlinear systems with time-delay is studied. Based on choosing a suitable Lypunnov-krasovskii functional, the stability of the error dynamic for one-sided Lipschitz nonlinear systems with time-delay is analyzed by using the linear matrix inequality theory. Then, the signal tracking controller which satisfies the H∞ tracking error performance index is designed by using the Schur complement. The simulation results are presented to illustrate the effectiveness of the proposed approach.