Robust Dissipation Control For Uncertain Linear Systems

Dissipative systems theory has been proposed since 1970s. It plays an important role in the study of system stability. Its essential content is being a nonnegative energy function, which makes the energy consumption of the system, is less than the energy provision. Uncertainty is very important notion in the robust control theory, and uncertainty is the result of that we use a relative simple mathematic model to replace a complex real system and we are lack of enough knowledge to the properties or inside details of the real systems. Meantime, time delay conditions are widely occurred in the real control systems, the existence of time delay makes it more complex and difficult to do analysis and synthesis for control systems, therefore, the research for time delay systems is always a hot issue in the field of control engineering. The main study aim of the thesis is to study the dissipation control for uncertain time delay systems with a full supply rate and LMI technique.Firstly, we introduced the programming process of the robust control theory, types of uncertainty and time delay, gave the detail description of dissipation and its mathematical expression, and we introduced several important lemmas, such as Schur Lemma; also, we introduced the notion of quadratic stability and paid more attentions to quadratic stability questions of uncertain time-delay system.Next, we studied some different models of uncertain time-delay system separately. For the first, we discussed the dissipative control problem for state feedback controller design for a class of uncertain time-delay systems based on the full supply rate, which built a state feedback controller in order to made the closed loop system strictly dissipative. The state feedback controller was built by the analysis for the linear system with norm bounded uncertainty and independent time-delay, then turned the problem into the expression with the form of linear matrix inequality which was easily solved by the LMI Box in the Matlab program. For the second, we discussed the dissipative control problem for a class of uncertain linear system with multi-varying-delay viz. the system with many time-delays for state and the delays were varying with time. We derived sufficient condition of strictly dissipation for such system by the careful study for the class of uncertain linear system with multi-varying-delays. At last, we considered the dissipative control problem for a class of uncertain time-delay nonlinear system which satisfied Lipschitz nonlinear conditions. Then we derived sufficient condition of strictly dissipation for such class systems in the form of linear matrix inequality, which was obtained by the Schur lemma and using the two conditions of Lipschitz assumptions.