Some Stability Results for General Linear Lumped-Parameter Dynamic Systems

Abstract

A technique is presented for stability of equilibrium of general, linear, lumped-parameter dynamic systems. Liapunov functions are used to develop stability conditions that are direct in terms of the mass, damping, and stiffness matrices. The significance of what is presented here is twofold. First, this technique can be applied to general asymmetric systems. Second, it offers direct conditions that can easily be programmed on a digital computer to handle high-order systems. Many previously developed results, such as the KTC theorem and its extensions, are mentioned. Next, it is shown that the present study may provide broader applications because general systems are included and a more convenient approach is offered. Examples are used to illustrate the validity and applications of the presented results.