Stochastic analysis of dynamical systems with delayed control forces

Reduction of structural vibration in actively controlled dynamical system is usually performed by means of convenient control forces dependent of the dynamic response. In this paper the existent studies will be extended to dynamical systems subjected to non-normal delta-correlated random process with delayed control forces. Taylor series expansion of the control forces has been introduced and the statistics of the dynamical response have been obtained by means of the extended Itô differential rule. Numerical application provided shows the capabilities of the proposed method to analyze stochastic dynamic systems with delayed actions under delta-correlated process contrasting statistics of response with estimates from Monte-Carlo (MC) simulation.