Uniform asymptotic stability of time-varying damped harmonic oscillators

摘要

This paper presents sufficient conditions which guarantee that the equilibrium of the damped harmonic oscillator is uniformly asymptotically stable, where is locally integrable. These conditions work to suppress the rapid growth of the frictional force expressed by the integral amount of the damping coefficient . The obtained sufficient conditions are compared with known conditions for uniform asymptotic stability. Two diagrams are included to facilitate understanding of the conditions. By giving a concrete example, remaining problems are pointed out.