Robust H_∞ Control For Uncertain Time-delay Systems

In the control system of analysis and research process, adopting exact mathematical models to reflect a practical controlled object is almost impossible. On the other hand, in a lot of practical industrial engineering control systems, the lag phenomenon exists everywhere, and these delay existence can cause the system to unstable or the dynamic response of the system performance degradation, cannot satisfy the system normal operation requirements. Therefore, the uncertain time-delay systems research not only has important theoretical significance and practical engineering meaning, but also the present control theory research of one of the hotspots.In recent years, for robust control theory study, there are many conclusions, but still has many problems to a progressive research. In this paper, on the basis of previous work, based on the Lyapunov stability theory, by using the linear matrix inequality and integral inequality analysis tools, complex uncertain time-delay systems of robust h-infinity control problem, main content as follows:1. Continuous uncertain linear systems with time-varying state delays and time-varying input delays are studied. Using linear matrix inequality (LMI) and integral inequality approach, sufficient conditions of uncertain time-varying systems and time dependent controller H_∞design method are obtained. Conclusion without hypothesis on system matrix is obtained through Krasovskii Lyapunov function method. And the simulation results show the effectiveness of the controller.2. Discrete uncertain linear systems with time-varying state delays and time-varying input delays are studied.. Sufficient conditions of robust stability of uncertain discrete delay systems and H_∞controller design method are obtained by Lyapunov function and linear matrix inequality approach. And the simulation results show the effectiveness of the controller.3. Continuous uncertain linear systems with state time-delay and input time-delay is considered. Conditions for robust asymptotic stability of continuous system and H_∞controller based on state estimation are provided by using Lyapunov function under the situation that the system state can not be directly measured. And simulation results prove it works.4. Discrete uncertain linear systems with state time-delay and input time-delay at the same time is studied. Conditions for robust asymptotic stability of discrete system and H_∞controller based on state estimation are provided by using Lyapunov function under the situation that the system state can not be directly measured. System parameters are optimized and minimumγallowed is got, along with simulation results prove it works.