Effect of Correlation on the Almost-Sure Asymptotic Stability of Second-Order Linear Stochastic Systems

Abstract

A method of obtaining a sufficient almost-sure (a.s.) asymptotic stability condition for second-order, linear systems with both ergodic damping and stiffness coefficients is presented. The probabilistic property of the correlation between the damping and stiffness coefficients is taken into account. A sufficient condition for a.s. asymptotic stability is derived and numerical results are presented for the case of Gaussian noise coefficients. Results obtained in some of the previous investigations are included in the present study as special cases.