Robust Dynamical Order Assignment For Linear Descriptor Systems

Descriptor systems provide us a more general description of physical systems, and this description is of great advantage 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. Because 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 dynamical order assignment and robust dynamical order assignment by derivative input feedback of descriptor systems.Firstly, the background, structure, development and research methods of descriptor systems are introduced. The problem of derivative feedback control of descriptor systems is studied. The method of regional pole placement by derivative feedback control is explained. And the robust stability of singular systems, the stability and Lyapunov equation of the discrete singular systems are introduced.Secondly, the problem of the dynamical order assignment of the singular systems is studied by derivative feedback control. The approach is based on an ability to adjust the number of infinite non-dynamical modes of the system within a permissible range. The solution is obtained by imbedding the descriptor-space problem in an equivalent state-space problem where a zero eigenvalue with a prescribed geometric multiplicity is assigned to linear state system by proportional feedback control. The conclusion in this paper can handle the dynamical order assignment of the singular system. Finally, an example is given to illustrate the validity of our method.At last, the problem of dynamical order assignment of the uncertain singular system is investigated. Through the robust stabilization of singular systems being investigated, the problem is transformed into the zero eigenvalue assignment of the equivalent augmented system. The robust dynamical order assignment is implemented by the stability and Lyapunov equation of the corresponding discrete system. Finally, an example is given to illustrate the validity of our method.