Yitshak M. Ram

Orthogonality and partial pole assignment for the symmetric definite quadratic pencil

Abstract The eigenvectors of a symmetric matrix can be chosen to form an orthogonal set with respect to the identity and to the matrix itself. Similarly, the eigenvectors of a symmetric definite linear pencil can be chosen to be orthogonal with respect to the pair. This paper presents the three sets of matrix weights with respect to which the eigenvectors of the symmetric definite quadratic pencil are orthogonal. One of these is used to derive an explicit solution of the partial pole assignment problem by state feedback control for a control system modeled by a system of second order differential equations. The solution may be of particular interest in the stabilization and control of flexible, large space structures where only a small part of the spectrum is to be reassigned and the rest of the spectrum is required to remain unchanged.

Receptance Method in Active Vibration Control

The pole/zero assignment problem is addressed using a method based on measured receptances. The approach, which is well known in passive structural modification, has not been used before in active vibration control. A number of significant advantages are claimed over the conventional state-space approach that uses the mass, damping, and stiffness matrices formed, for example, by finite elements. In fact, because the method is based solely upon measured vibration data, there is no need to evaluate or to know the M, C, and K matrices. It is demonstrated that all the poles may be assigned actively by the equivalent of a rank-1 modification to the dynamic stiffness matrix of the system. The assignment of zeros has a special significance in vibration suppression, because the vibration response at coordinatep vanishes completely when sinusoidal excitation is applied at coordinate q at the frequency of a zero of receptance H nn . A pole ofH pq may be eliminated by assigning a zero at the same frequency.

An inverse eigenvalue problem for the symmetric tridiagonal quadratic pencil with application to damped oscillatory systems

A method is presented which constructs an n by n tridiagonal, symmetric, quadratic pencil which has its

Transcendental Eigenvalue Problem and Its Applications

2n

Inverse eigenvalue problem for a modified vibrating system

eigenvalues and the

Physical parameters reconstruction of a free-free mass-spring system from its spectra

2n - 2

Dynamic Absorption by Passive and Active Control

of its

Mass and stiffness modifications to achieve desired natural frequencies

n - 1

An affine inverse eigenvalue problem

-dimensional leading principal subpencil prescribed. It is shown that if the given eigenvalues are distinct, there are at most

On Some Eigenvector-Eigenvalue Relations

2^n ( 2n - 3 )!/( n - 2 )!