ON THE ALMOST-SURE ASYMPTOTIC STABILITY OF SECOND ORDER LINEAR STOCHASTIC SYSTEM

A method for obtaining a sufficient almost-sure stability condition for second order linear systems with an ergodic stiffness coefficient is presented. In this method, a special Lyapunov function for achieving functional optimization is constructed and the probabilistic property of the derivative process of the stiffness is taken into account. A sufficient condition for almost-sure asymptotic stability is derived and numerical results are presented for the cases of Gaussian noise and periodic noise coefficient. The results obtained here are an improvement over previously available results for linear systems with stochastic stiffness.