Robust Control Of Uncertain Time-Delay Systems

With social development and the progress of science and technology, many complex systems exist in nature and modern society, such as engineering, living beings and society economy. It is unavoidable to include uncertain parameters and disturbances in practical control systems due to modeling errors, measurement errors, linearity approximations, and so on.In addition, because of the executing time of actuator and sensor and the communication time of network, there are also time delays in the closed-loop systems, such as network control system and teleoperation system etc. At the same time, the characteristic equations of the controlled systems with time delays are transcendental equations and belong to infinite dimensional systems, so it is difficult to study the time delay systems in mathematics theory and also difficult to obtain good performance for the time delay systems using the controller designed by classical control theory. So study for the time delay systems has high theoretical and practical significance.Because time delays and uncertainties exist widely and both of them may cause instability and performance deterioration if not dealt with properly, it is necessary and significant to study the control for the nonlinear uncertain time delay systems. This master thesis focuses on some robust Performance analysis and robust controller design with LMI approaches together with Lyapunov stability theory .In this paper, based on the Lyapunov stability theory and linear matrix inequalities (LMIs), we mainly study the Problems of robust stability analysis and robust controller design for time-delay systems with nonlinear uncertain Parameter respectively. The designed controllers in this paper are feasible and the conservatives of the proposed methods are reduced considering more delay information. The main contents are as follows:1. The problem of robust stabilization via nonlinear state feedback is studied for time-delays systems with output uncertain. To solve this problem, the auxiliary variables and generalized states methods are used to prove the asymptotic stability of the system. Finally an illustrative example verified the effectiveness and rationality of the conclusion. 2. The problem of robust stabilization for uncertain multiple time-delays systems with nonlinear perturbation is proposed. Firstly, based on Lyapunov stability theory, the delay dependent stabilization criteria for autonomous system is developed. Secondly, robust controller is given by analyzing the stability of class-loop system. The sufficient condition for the existence of the state feedback controller is derived in term of linear matrix inequalities. It is finally shown by two examples that the method presented is this paper can reduce the conservativeness of the results, which indicates the validity of the proposed method.3. The problem of robust stabilization via output feedback is studied for nonlinear uncertain systems with time-delay. On the condition that nonlinear function are bounded. By using the linear matrix inequality (LMI), a sufficient condition of the output feedback stability about the nonlinear uncertain systems with time-delay is obtained and then the design method of its robust stability is also given in it. Finally, an example is employed to illustrate the validity and effectiveness of the proposed method.4. The problem of observer-based robustly stable controller is studied for time-delay systems with a class of nonlinear uncertainty. On condition that the nonlinear uncertain functions are gain-bounded, they prove a sufficient condition for the robust stability of augmented system based on Lyapunov theory. The result obtained is an extension of the linear case of the problem.The conclusion and the perspective of future research are given at the end of the paper.