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Displaying similar documents to “Stability of periodic solutions of first-order difference equations lying between lower and upper solutions.”

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....

Continuous-time periodic systems in H 2 and H . Part I: Theoretical aspects

Patrizio Colaneri (2000)

Kybernetika

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The paper is divided in two parts. In the first part a deep investigation is made on some system theoretical aspects of periodic systems and control, including the notions of H 2 and H norms, the parametrization of stabilizing controllers, and the existence of periodic solutions to Riccati differential equations and/or inequalities. All these aspects are useful in the second part, where some parametrization and control problems in H 2 and H are introduced and solved.