Ordinary Differential Equations and Dynamical Systems Vol2 · Problem 3.16

Nonautonomous Linear Systems

Mathematics — Calculus · asymptotic-stability-nonlinear-perturbation

Problem

Let

\phi

be a

C^1

function on

\mathbb{R}

with

\phi(0) = \phi'(0) = 0

. Let

a, b > 0

. Prove that the origin is asymptotically stable for the system

x' = y, \quad y' = -ax - by + \phi(x).