The Robust Control Of A Class Of Singularly Perturbed Systems

The singularly perturbed theory developed rapidly in mathematics for several decades, also made a breakthrough in the field of control, and has been continuous improvement associated with the development of control theory. Meanwhile the linear matrix inequality technology in control of areas used more and more widespread in recent years. However, the application is rare in the singularly perturbed system. This thesis will focus on the singularly perturbed systems and try to integrate the LMI methods to do the research. To sum up, the major works in this thesis are as follows:1. The basic concepts, background, purpose and significance of the singularly perturbed systems are introduced.2. Using Lyapunov stability theory and several related inequalities, by constructing suitable Lyapunov function, derive the sufficient condition of the existence of the state feedback controller. Furthermore, give the feedback controller design method, and give the controller parameters trough the feasible solution of linear matrix inequalities. And then, research the situation with the feedback control of the time delay perturbed systems.3. Using Lyapunov stability theory, combing with the inequalities processing techniques, then the problems are converted to solve LMI. Give the feedback controller design methods and performance index, the controller makes the system stability and the performance function has the specified upper bound.