Mathematics

On robust stability in the problem of inverted pendulum

G. V. Demidenko^a, Myagkikh Kseniya S<sup>b

a</sup> Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^b Novosibirsk State University

Abstract: The paper considers a nonlinear equation of motion of a pendulum the suspension point of which performs high-frequency harmonic oscillations. The problem of robust stability for the upper equilibrium position is studied. Conditions for perturbations of the equation coefficients are established, under which the corresponding stationary solution is exponentially stable. Estimates for attraction sets are given and estimates for stabilization rates of solutions at infinity are obtained.

Keywords: robust stability, exponential stability, attraction set, Lyapunov differential equation

UDC: 517.925.51

Received: 15.10.2024
Accepted: 06.12.2024

DOI: 10.25587/2411-9326-2024-4-16-28