Robust Control For A Class Of Nonlinear Systems With Time Delay In The Input

The control problem of nonlinear time delay systems has been the hot and difficult topic in the present control theory investigation. The existence of time delay renders the control problem of nonlinear systems more complex and difficult. The robust control problem of nonlinear systems with time varying delays in the state and input will be focused on in this dissertation. For the systems with different assumptions on the nonlinear uncertainty, the corresponding feedback controllers are presented.We first consider a class of nonlinear time delay systems with the bound functions of uncertainties in the parameterized form. Moreover, the uncertainties arising from the state, delayed state and input are involved and assumed to be nonlinear perturbations with known bounds of the weighted norm of the state and delayed state vectors. A robust stabilizing controller is designed by means of the Lyapunov-Krasovskii functional stability theory, which can stabilize the uncertain nonlinear systems. From the simulation results, we can conclude that the proposed controller design methodology leads to a larger class of uncertain systems can be stabilized than the existing methods.Furthermore, we consider a class of uncertain nonlinear systems with time varying delays in both the states and the input. The nonlinearities of the systems are assumed to be bounded by a weighted norm of the state. An asymptotically stabilizing adaptive controller is derived by means of the construction of an appropriate Lyapunov-Krasovskii functional and the use of linear matrix inequalities techniques and the adoption of an adaptive factor. Finally, the effectiveness of the proposed controller is explained and demonstrated on some numerical examples.