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

Abstract

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.