Partial Eigenvalue Assignment Problem For Linear Systems

Using the theories and methods of algebraic inverse eigenvalue problem,we discuss the partial eigenvalue assignment and eigenstructure assignment problem of the first order linear systems and the partial eigenvalue assignment problem of high order linear systems.The main contents can be stated as follows:For the first order linear control systems with time delay,we give the solvable conditions and its numerical solutions to the partial eigenvalue assignment problem for the single-input case.For the multi-input case,we propose a multi-step method for solving this problem by which the unwanted eigenvalues are moved to desired values and all other eigenpairs remain unchanged.For the first order linear control systems,consider the limited degree of freedom in the finite element model and the limited number of sensors to measure the structural response,the order of the measured eigenvectors is usually much less than the degree of freedom of the finite element model.In this paper,we give a mode shape expansion method of incomplete modal data(eigenvectors)and propose a method for solving the partial eigenstructure assignment problem with incomplete modal data.For the high order linear control systems,based on the orthogonality relations,the unwanted eigenvalues are moved to desired values and all other eigenpairs remain unchanged.Using the inverse of Cauchy matrix,we give the solvable conditions and its numerical solutions to the partial eigenvalue assignment problem for the single-input case.For the multi-input case,we propose a multi-step method for solving this problem.Numerical examples show that the proposed algorithms are effective.