Asymptotic Stability of Solutions to a Class of Second-Order Delay Differential Equations
Г. В. Демиденко, И. И. Матвеева
Abstract
We consider a class of second-order nonlinear delay differential equations with periodic coefficients in linear terms. We obtain conditions under which the zero solution is asymptotically stable. Estimates for attraction sets and decay rates of solutions at infinity are established. This class of equations includes the equation of vibrations of the inverted pendulum, the suspension point of which performs arbitrary periodic oscillations along the vertical line.
Topics & Concepts
MathematicsMathematical analysisNonlinear systemInfinityClass (philosophy)Exponential stabilityDifferential equationPendulumEquilibrium pointStability (learning theory)Zero (linguistics)Delay differential equationOrder (exchange)Suspension (topology)PhysicsPure mathematicsArtificial intelligenceEconomicsComputer scienceHomotopyFinanceQuantum mechanicsMachine learningPhilosophyLinguisticsDifferential Equations and Numerical MethodsAdvanced Mathematical Modeling in EngineeringStability and Controllability of Differential Equations