A New Algorithm For Pole Assignment In Description System Via State Feedback

The pole assignment for descriptor systems is a very important problem in the design of the control systems, and has been studied widely. In recent years, with the maturity and development of the descriptor system theory, it not only proposed more requirement on mixed pole assignment, but also make the research of mixed pole assignment having far-reaching significance.In this paper, we make linear time-invariant descriptor system as the research object, a new algorithm for pole assignment in descriptor system via state feedback is presented. We combined the existing approach for infinite and finite pole assignment in descriptor system via state feedback with matrix decomposition and compression knowledge which we learned, so as to propose a new algorithm for pole assignment in descriptor system via state feedback. The algorithm is made up by three parts. Firstly, with the help of orthogonal row/column compressions, we can finish part of infinite pole assignment. As we know the matrix row/column compression algorithm has good numerical stability, then the algorithm we used to finish part of infinite pole assignment has fine numerical characteristics, therefore compress the original system into a low-dimensional system by this way. Secondly, we complete other infinite and finite pole assignment on low-dimensional system through the existed methods, so there are less computational work of assignment, and less computational errors in low dimensional system than those in original system. Thirdly, the algorithm of whole feedback matrix is obtained by means of row/column compression and mixed pole assignment. Finally, the numerical example in the last part of this paper indicates the effectiveness, simplicity and good numerical characteristics of this algorithm.