Almost sure asymptotic stability of an oscillator with delay feedback when excited by finite-state Markov noise

作者：Lingala Nishanth^*; Namachchivaya N Sri; O' Reilly Oliver M; Wihstutz Volker

来源：Probabilistic Engineering Mechanics, 2013, 32: 21-30.

DOI：10.1016/j.probengmech.2012.12.008

• Almost-sure stability
• Delay differential equation
• Lyapunov exponent
• Chatter

An oscillator of the form q(t)+2 zeta(q) over dot(t)+q(t)= -kappa[q(t)-q(t-r)] is unstable when the strength of the feedback (kappa) is greater than a critical value (Ice). Oscillations of constant amplitude persist when kappa = kappa(c). We study the almost-sure asymptotic stability of the oscillator when kappa = kappa(c) and the system is excited by a two-state Markov noise. For small intensity noise, we construct an asymptotic expansion for the maximal Lyapunov exponent.

• 出版日期2013-4