Proportional And Derivative Output Feedback Control Of Singular Systems

Singular systems provide us a more general description of physical systems, and this description is of great advantages than normal systems. Consequently and undoubtedly, singular systems have led us into a virgin land which is full of challenges and opportunities. Recently, more and more scientists and engineers are becoming absorbed in this field and, therefore, lots of meaningful results have been concluded. However, the controllers are designed based on proportional state feedback, proportional output feedback and dynamical output feedback, and there is not much attention to the controller design based on derivative feedback. Beause of the specialization of derivative matrix of descriptor systems, some performances could not be realized by proportional feedback, but it could be realized by derivative feedback under some conditions, which implies the superiority of derivative feedback. In this paper we investigated the problem of proportional and derivative output feedback of singular systems.Firstly, The problem of admissibility related to singular systems by PDOF (proportional and derivative output feedback) is investigated. The closed loop system is admitted by proportional and derivative output feedback. And the step of computing feedback gain is given. Finally, an example is given to illustrate the validity of our method.Secondly, The problem of the H∞output feedback of continuous singular systems by proportional and derivative output feedback is investigated. The objective is to design proportional and derivative output feedback controller such that the closed loop system could be admissable and be satisfied to H∞performance. The method of H∞controller design is presented. The conclusion in this paper can handle singular systems with impulse. Finally, an example is given to illustrate the validity of our method.At last, The problem of the robust control of uncertain singular systems by proportional and derivative output feedback is investigated. Through the robust stabilization of singular systems being investigated, the closed loop system is to be robust stabilized by proportional and derivative output feedback. And the step of computing feedback controller is given. Finally, an example is given to illustrate the validity of our method.