Robust Control Of Time-Delay Systems With Nonlinear Uncertain Parameters

Problems of robust stability analysis and robust controller design for time-delay systems with nonlinear uncertain parameters are studied in this paper. Since 1970s, robust stability analysis and robust controller design for time-delay systems have always been the main contents of the research in the control theory. A more deep investigation into such subjects would not only perfect the foundation of control theory, but also promote the implementation of such theory in practice.Mainly contents in this paper include the following two parts: robust stability analysis and robust controller design.Our work on the problem of robust stability analysis for time-delay systems with nonlinear uncertain parameters are mainly concerned about the following three aspects:Firstly, using Lyapunov method and complex Lyapunov method, we give the conditions of the robust stability for the corresponding system under the assumption that uncertainty is high structured uncertainty. We also derive the sufficient conditions of robust stability by rank-1 decomposition of the matrix under the assumption that uncertainty is matrix polytope structured uncertainty. Both of the derived principles are time-delay independent.Secondly, using Lyapunov method and Razumikhin-type asymptotic stability theory, we give the conditions of robust stability under the assumption that uncertainty is unstructured uncertainty and norm bounded uncertainty, which are time-delay dependent.Thirdly, assuming that uncertainty is unstructured uncertainty, we obtained the conditions of robust stability based on the solutions to the system and the Bellman-Gronwel inequality.Our work on the problem of robust controller design for linear time-delay systems with nonlinear uncertain parameters are mainly concerned about thefollowing three aspects:Firstly, based on Lyapunov theory and using linear matrix inequation (LMI) method, we put forward a plan to design the state feedback controller of the system with high structured uncertainty and matrix polytope structured uncertainty.Secondly, according to the system which is matrix polytope structured uncertainty, we give a plan to design the state feedback controller of time-delay.Thirdly, according to the norm bounded uncertainty, we can stabilize the system using output feedback controller. In this part we use the linear matrix inequation method.In the end, we do some numerical experiments examples and use Matlab for simulation to testify the effectiveness of our results.