Stability analysis of vibro-impact systems with stochastic parameters

This paper is concerned with a general method of stability analysis of vibro-impact systems with stochastic parameters. First of all, based on establishing the Poincare map of n-1 periodic motion, the stability conditions of n-1 periodic motion for the vibro-impact systems are derived. Then we put emphasis on analyzing the stability of n-1 periodic motion for the vibro-impact systems with stochastic parameters. By deriving the expectation and variance and determining the range of probability distribution of Jacobian matrix G(s) of the Poincare map of n-1 periodic motion, we finally obtained the conditions of robust stableness, non-robust stableness and unstableness for n-1 periodic motion. At the end, the analytical method is confirmed by an example.