H₂and H_∞Optimal Control Problem By Output Feedback For Singular System

Singular System is a kind of control system of more general. It has been developed sufficiently from1980s.But the development of H2and H∞optimal control of singular system is more slowly than normal system. In many practical problems, the states of the system are not directly measured, even if can be measured, but the cost is large, often using the output feedback stabilization and optimization system. So we mainly discuss the H2and H∞optimal control problem by output feedback for singular system.Firstly, we discuss H∞optimal control. For a singular system model, the static and dynamic output feedback controllers are derived; for a singular system model with uncertainty, the dynamic output feedback control is derived, thereby all making the closed-loop systems admissible, and in the meanwhile, make sure that the H∞norm is less than the given value. Then sufficient condition or necessary and sufficient condition is given. Finally the corresponding numerical examples are present in order to illustrate the effectiveness of the proposed method.Secondly, we discuss H2optimal control. For a singular system model and with uncertainty, the dynamic output feedback controllers are derived, thereby all making the closed-loop systems admissible, and in the meanwhile, make sure the H2norm is minimum. Then sufficient condition or necessary and sufficient condition is given. Finally the corresponding numerical examples are present in order to illustrate the effectiveness of the proposed method.Lastly, a summary of this thesis is given. At the same time, we give an expectation for the future work.