A Lyapunov Function for Systems Whose Linear Part is Almost Classically Damped

[+] Author and Article Information
S. J. Cox

Department of Computational and Applied Mathematics, Rice University, P.O. Box 1892, Houston, TX 77251

J. Moro

Departamento de Mathematicas, Universidad Carlos III, Butarque 15, Leganes (Madrid), Spain

J. Appl. Mech 64(4), 965-968 (Dec 01, 1997) (4 pages) doi:10.1115/1.2789007 History: Received September 16, 1996; Revised May 06, 1997; Online October 25, 2007


We show that one may construct a Lyapunov function for any classically damped linear system. The explicit nature of the construction permits us to show that it remains a Lyapunov function under both perturbation of the linear part and introduction of a nonlinear term. We apply our findings to a stability analysis of the discrete, as well as continuous, damped mechanical transmission line.

Copyright © 1997 by The American Society of Mechanical Engineers
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