Robust Controller Design And Its Application For Linear Uncertain Systems

Some unknown elements always exist in the analysis process for the control systems, such as unmodeled dynamics, parametric uncertainties, change of the operating environment, model reduction and linearization approximations, etc., or external disturbance. So it is significative to study the disturbance process or the uncertain systems. The emergence and the development of the robust control theory was just in such environment, and it is becoming an important research field of the control theory and its practice applications. The robust control consists of two important aspects: (1) The robustness and the stability. (2) The robust synthesis. In this paper robust controller for uncertain systems and time-delay systems was designed, using Lyapunov stability theory and linear matrix inequality theory, try to avoid the effect of the modeling error in system and the disturbed signal from the system and outside. By using the Matlab software to simulink for systems. The work of this dissertation mainly addresses the issues for robust control of linear uncertain systems, which include stability, quadratic stability, iterative learning control, H∞control, etc.. Combine with the conditions discussed in upper section, the stability of linear uncertain systems was firstly studied. Based on the concept of quadratic stability of the systems, the sufficient conditions of quadratic stability for a class of linear uncertain systems were given. Considered the importance of studying the delay systems, the stability of many delay uncertain systems was studied and some results have been gained. the sufficient condition of delay-independent quadratic stabilization for a class of uncertain linear systems with time-delay was given, with this understanding, the problem of delay-dependent quadratic stabilization for a class of uncertain linear systems was discussed, it could be translated into the problem of solving an linear matrix inequality, and the conclusion was validated using the LMITOOLBOX. The sufficient condition of quadratic stabilization for a class of uncertain linear multi-delay systems was given based on LMI. Secondly the robust stabilization of the linear uncertain systems was considered, which are the robust synthesis has been mentioned in upper section, the problems such as the quadratic stabilization for a class of linear uncertain systems and delay systems were discussed based on states feedback, and the sufficient condition for the existing of the robust stabilization controller was given based on LMI, it is easy to find the solution of controller using the LMI toolbox, it overcame the Riccati's shortcomings for solving these problem. The problem of decentralized feedback stabilization for a class of interconnected systems with delay in the interconnect terms was considered, and the sufficient condition for the existing of the stabilization controller was given based on LMI, and an example was given to validated the conclusion. Finally the problem of the iterative learning control of a class of linear delay systems was firstly studied, the control problem of the iterative control of a class of linear delay systems was converted into the static output feedback control of a class of linear delay systems, and gave the sufficient condition for the converging of the systems based on LMI, also the structure of the iterative learning controller was given. The robust H∞control for a class of linear uncertain systems with delays based on PI control laws were considered also in our paper, the designing of PI control laws could be converted into the problem of designing the static output feedback controller, the structure of the controller was presented by using of solving the LMIs, and the results were validated with some example.