导　　师： 王兴涛

学科专业： 0701

授予学位： 博士

作　　者： ;

机构地区： 哈尔滨工业大学

摘　　要： 特征值配置问题是系统设计的重要问题之一，该问题在高阶系统上的研究是一类更一般化、应用更为广泛的控制设计问题。本文以线性系统为研究对象对现有理论作了进一步讨论，研究主题是高阶系统的状态反馈特征值配置，内容包括单输入特征值配置、多输入特征值配置，特征结构配置、时滞系统特征值配置及时滞系统稳定性分析。主要成果体现在以下几个方面： 对高阶线性系统状态反馈部分特征值配置问题，利用系统矩阵与开环特征向量间的正交关系，确定了高阶线性系统状态反馈部分特征值配置无溢出的条件。将特征值配置问题转化为矩阵多项式求解问题，实现单输入高阶线性系统状态反馈部分特征值配置。随后，多输入系统部分特征值配置问题被划分为多个单输入系统特征值配置问题，将所得单输入特征值配置理论应用其中，完成多输入系统部分特征值配置，并给出实际算例，验证了算法的有效性。 在控制矩阵未给定的情况下，对任意给定的特征值与特征向量，探讨如何设计控制矩阵与反馈矩阵的问题，给出了同时确定控制矩阵与反馈矩阵的方法，建立了求解该问题的算法。分析了部分特征结构配置实解的存在性，为该问题的后续研究奠定理论基础。 对时滞高阶线性系统的部分特征值配置问题，分别给出了单输入、多输入情形下求解该问题的算法。对于单输入系统，利用系统矩阵与开环特征向量间的正交关系，给出了部分特征值配置满足无溢出性质的充要条件，建立了求解单输入时滞系统部分特征值问题的算法。对于多输入时滞系统部分特征值配置问题，给出了多步混合法和响应矩阵法。多步混合法延续了无时滞算法的特点。响应矩阵法可以在系统矩阵信息未知的情况下，通过测得的响应值实现特征值配� 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

关 键 词： 高阶系统 部分特征值配置 状态反馈 矩阵多项式 无溢出性 时滞系统稳定性

领　　域： [自动化与计算机技术] [自动化与计算机技术]