Analysis And Synthesis For Time-Delay Systems With Actuator Saturation

It is well known that time delay phenomena exist in many practical control systems, such as transmission systems, communication systems, power systems, etc. Time delay often has adverse effects on the performance and even may cause oscillation, divergence and instability to systems. Actuator saturation phenomenon is another common problem existing in control systems. Stability analysis of systems with actuator saturation has been widely studied and many efforts have been made to enlarge the estimate of the domain of attraction. In many practical control systems, time-delay and actuator saturation sometimes occur together, which makes the control system more complex and more difficult to control. There have been some papers addressing the systems where these two problems co-exist. However, these results still have much conservatism. Based on the previous works, the problems of stability analysis, state-feedback controller design, H_∞state-feedback controller design for time-delay systems with actuator saturation are investigated in this thesis.Firstly, this thesis summrizes the main results in the field of stability analysis of time-delay systems with actuator saturation, and points out the defeiciency of the existing results, that is, most of the results can only be applied to systems with constant time delay and althought some results can handle time varying delay in a range, the conservatism of the results is still large. Base on this, the problems of stability analysis and stablization of continuous time-delay systems with actuator saturation are studied, and new stability conditions, methods of state feedback controller design and conditions of estimating the domain of attraction are obtained in this thesis. The stability criteria are proposed in terms of linear matrix inequality, which could be solved by MATLAB tools. The free-weighting matrix technique and the delay partitioning idea are employed to handle the time-delay term while the auxiliary feedback matrix idea to the saruration term. The stability criteria proposed in this thesis can be applied to not only continuous constant time-delay systems with actuator saturation, but also continuous time-varying delay systems with actuator saturation. Numerical examples demonstrate that the proposed methods are less conservative than other existing ones in the literature.Secondly, stability analysis, state-feedback controller design and the estimate of the domain of attraction for discrte time-delay systems with actuator saturation are also studied in this thesis. By combining the improved free-weighting matrix technique with the convex polytope method, less conservative stability results have been obtained via the delay-range-dependent approach. The stability criteria can handle both constant time delay and time varying delay in a range. Numerical simulations verify the effectiveness of the proposed methods.Thirdly, the problem of H_∞state-feedback controller synthesis for continuous time-delay systems with actuator saturation is investigated. At first, the conditions which guarantee the state trajectory of the closed-loop system remains within an ellipsoid when the disturbance signal exists are presented; then a new method for H_∞state-feedback controller design is proposed. Illustrative examples demonstrate the effectiveness of the theoretical results.