Uniform asymptotic stability of time-varying damped harmonic oscillators

This paper presents sufficient conditions which guarantee that the equilibrium of the damped harmonic oscillator
x”+ h(t)x’+ ω2x = 0
is uniformly asymptotically stable, where h : [0,∞) → [0,∞) is locally integrable.
These conditions work to suppress the rapid growth of the frictional force expressed by the integral amount of the damping coefficient h. 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.