The Lyapunov stability for the linear and nonlinear damped oscillator with time-periodic parameters.

Chu, Jifeng; Xia, Ting

Displaying similar documents to “The Lyapunov stability for the linear and nonlinear damped oscillator with time-periodic parameters.”

On Lyapunov stability/instability of equilibria of free damped pendulum with periodically oscillating suspension point

Jiří Šremr (2025)

Applications of Mathematics

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We discuss Lyapunov stability/instability of both lower and upper equilibria of free damped pendulum with periodically oscillating suspension point. We recall the results of Bogolyubov and Kapitza, provide new effective criteria of stability/instability of the equilibria of pendulum equation, and give the exact and complete proofs. The criteria obtained are formulated in terms of positivity/negativity of Green's functions of the periodic boundary value problems for linearized equations....

Stability and Boundednessof the Solutions of Non Autonomous Third Order Differential Equations with Delay

Moussadek Remili, Lynda Damerdji Oudjedi (2014)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In this article, we shall establish sufficient conditions for the asymptotic stability and boundedness of solutions of a certain third order nonlinear non-autonomous delay differential equation, by using a Lyapunov function as basic tool. In doing so we extend some existing results. Examples are given to illustrate our results.

The structural influence of the forces of the stability of dynamical systems.

Lupu, Mircea, Florea, Olivia, Lupu, Ciprian (2009)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

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The stability cone for a matrix delay difference equation.

Kipnis, M.M., Malygina, V.V. (2011)

International Journal of Mathematics and Mathematical Sciences

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Note to the Lagrange stability of excited pendulum type equations

Ján Andres, Staněk, Svatoslav (1993)

Mathematica Slovaca

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Variational Lyapunov method and stability theory.

Lakshmikantham, V., Liu, X., Leela, S. (1998)

Mathematical Problems in Engineering

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Stability and periodicity for linear differential equations with periodic coefficients

L. Erbe (1975)

Annales Polonici Mathematici

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Boundedness and asymptotic stability in the large of solutions of an ordinary differential system $y^{'} = f (t, y, y^{'})$ .

Venkatesulu, M., Srinivasu, P.D.N. (1992)

Journal of Applied Mathematics and Stochastic Analysis

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Stability of a class of adaptive nonlinear systems

Andrzej Dzielinski (2005)

International Journal of Applied Mathematics and Computer Science

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This paper presents a research effort focused on the problem of robust stability of the closed-loop adaptive system. It is aimed at providing a general framework for the investigation of continuous-time, state-space systems required to track a (stable) reference model. This is motivated by the model reference adaptive control (MRAC) scheme, traditionally considered in such a setting. The application of differential inequlities results to the analysis of the Lyapunov stability for a class...