Inverse Eigenvalue Problems Of Gyroscopic Systems

By means of the theories and methods of algebraic inverse eigenvalue problem,the model updating problem,the partial eigenvalue assignment problem and the minimum norm partial eigenvalue assignment problem of gyroscopic systems are investigated.The main contents can be stated as follows:For the model updating problem of gyroscopic systems,a new method for updating gyroscopic matrix by using output feedback technique is presented,and thus the optimal approximation solution which satisfies the eigenvalue equation and the skew-symmetric property is given under the Frobenius norm sense.A modified conjugate gradient method for simultaneously updating mass,gyroscopic and stiffness matrices by using output feedback control is proposed,and thus the optimal approximation solution which satisfies the eigenvalue equation is given under the Frobenius norm sense.For the partial eigenvalue assignment problem of gyroscopic systems,we consider this problem by using the displacement,velocity and acceleration state feedback control.Based on the orthogonality relations and the property of Cauchy matrix,we give the solvable conditions and its numerical solutions of this problem for the single-input case.Then we propose a multi-step method for solving this problem for the multi-input case.For the minimum norm partial eigenvalue assignment problem of gyroscopic systems,by using receptance method and Kronecker product,we transform this problem into finding the minimum norm solution of the matrix equations and propose a modified conjugate gradient method for solving this problem.Numerical examples show the efficiency of the proposed algorithms.