Asymptotic Lyapunov stability with probability one of Duffing oscillator subject to time-delayed feedback control and bounded noise excitation

• Published in: Acta mechanica Vol. 208; no. 1-2; pp. 55 - 62
• Main Authors: Feng, Changshui, Zhu, Weiqiu
• Format: Journal Article
• Language: English
• Published: Vienna Springer Vienna 01.11.2009; Springer; Springer Nature B.V
• Subjects: Classical and Continuum Physics; Control; Differential equations; Dynamical Systems; Engineering; Engineering Thermodynamics; Exact sciences and technology; Feedback; Fundamental areas of phenomenology (including applications); Heat and Mass Transfer; Mathematics; Mechanical engineering; Numerical analysis; Numerical analysis. Scientific computation; Physics; Sciences and techniques of general use; Simulation; Solid Mechanics; Stochastic models; Structural and continuum mechanics; Theoretical and Applied Mechanics; Vibration; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Stochastic Average Method; Delay Feedback Control; Lyapunov Exponent; Digital Simulation; Large Lyapunov Exponent; Parametric excitation; Averaging method; Itô equation; Probabilistic approach; Random excitation; Lyapunov method; Feedback regulation; Delay system; Noise control; State variable; Asymptotic stability; Non linear oscillator; Active system; Delay time; Duffing equation; Force control; Delay effect; Random vibration; Lyapunov function

The asymptotic Lyapunov stability with probability one of a Duffing system with time-delayed feedback control under bounded noise parametric excitation is studied. First, the time-delayed feedback control force is expressed approximately in terms of the system state variables without time delay. The...