Partial Eigenvalue Assignment In High-order Systems For State Feedback Control

Eigenvalue assignment problem is one of the important problems in system designs. The research of eigenvalue assignment problem in high order system is a kind of control design issue of more general applied background. Considering the linear system, the work of this dissertation mainly addresses the issue of state-feedback eigenvalue assignment in high order systems, which include eigenvalue assignment of single-input and multi-input system, eigenstructure assignment, eigenvalue assignment in time-delay system and stability analysis of time-delay system. The results of the dissertation are as follows:For eigenvalue assignment problem in high order linear systems for state feedback, by using the orthogonality relations between system matrices and open-loop eigenvec-tors, the condition of no-spillover property for partial eigenvalue assignment in high order systems are obtained, which lay a theoretical foundation for solving high-order eigenval-ue assignment problem. The equivalent transformations between eigenvalue assignment and matrix polynomial problem are developed, and an algorithm for single-input par-tial eigenvalue assignment of high-order systems for state feedback is established. Then, multi-input assignment problem is formulated as several successive single-input assign-ment problem. By using the single-input results, partial eigenvalue assignment of multi-input systems is achieved. By numerical experiments, the feasibility and effectiveness of the algorithm are verified.In the case of the assigned eigenpairs given arbitrarily, a method for getting the control matrix and the feedback matrices is explored in the condition of that the control matrix is unknown. The existence of the real solution for partial eigenvalue assignment problem is analyzed. These theories offer a theoretical foundation for future research.For partial eigenvalue assignment problems, algorithms for single-input and multi-input cases are given respectively. For single-input eigenvalue assignment problems, the sufficient and necessary condition of no-spillover property is verified. Then, an algorith-m for single-input partial eigenvalue assignment of high-order delayed systems for state feedback is proposed. For the multi-input case, we give the multi-step hybrid method and the receptance matrix method for solving this problem. Multi-step hybrid method is established, which inherit all the merits of the multi-step ones. The advantage of re-ceptance matrix method is that the approach is implementable with the measurements without the knowledge of system matrix. Moreover, the method of receptance also has small calculation and high freedom degree features. The feasibility and effectiveness of the algorithms are illustrated by numerical experiments. At last, the stability of high-order delayed system is analysed. For the analysis of high-order ordinary systems, the equiva-lent transformations between one-order approximate systems and high-order systems are established. The simple and effective method for analyzing the stability of time-delay systems is presented.