On the robust stability of stationary solutions to a class of Mathieu-type equations

TL;DR

This paper investigates the robust stability of stationary solutions in a class of Mathieu-type equations, providing conditions for stability under perturbations and estimates for attraction sets and stabilization rates.

Contribution

It introduces new criteria for the robust stability of stationary solutions in nonlinear Mathieu-type equations, including stability conditions and estimates for attraction and stabilization.

Findings

Derived conditions ensuring asymptotic stability under coefficient perturbations

Provided estimates for attraction sets of the zero solution

Established bounds on the stabilization rate of solutions

Abstract

We consider a class of nonlinear ordinary differential equations of the second order with parameters. We establish conditions for perturbations of the coefficients of the equation under which the zero solution is asymptotically stable. Estimates for attraction sets of the zero solution and estimates of the stabilization rate of solutions at infinity are obtained. Using these results, theorems on the robust stability of stationary solutions are proven.