On the Stability of Second Order Time Varying Linear Systems

[+] Author and Article Information
M. Tadi

Department of Mechanical Engineering, University of Colorado at Denver, Campus Box 112, P.O. Box 173364, Denver, CO 80217-3364mtadi@carbon.cudenver.edu

This is one way to ensure that the condition (i) in the theorem 1 is satisfied. When K̇=0 for t0, then Λ̇=Γ̇=0 for t0. The diagonal matrix of eigenvalues Γ is positive definite for all times and the terms in R(t) may change in such a way that 0R(t)dt< without K̇=0 for t0. But for simplicity we exclude these cases.

The condition K̇=0 for t0, is one way to ensure that limt=R(t)=0.

J. Vib. Acoust 128(3), 408-410 (Oct 28, 2005) (3 pages) doi:10.1115/1.2159042 History: Received July 01, 2005; Revised October 28, 2005

This note considers the stability of linear time varying second order systems. It studies the case where the stiffness matrix is a function of time. It provides sufficient conditions for stability and asymptotic stability of the system provided that certain conditions on the stiffness matrix are satisfied.

Copyright © 2006 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

Time response of the system for increasing damping



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