A common algorithm for random vibration and vibration control analysis of dynamic systems

Abstract As the inherent relationship between the Lyapunov equations and the Riccati equations, a common algorithm is established which can carry out both the mean square responses, which satisfy the Lyapunov equations, in the random vibration analysis of a dynamic system and the feedback gain matrix in the optimal control law, which satisfies the Riccati equations, in its vibration control problems. The algorithm is an iterative one, which is proved to be unconditionally stable and does not need to estimate the initial value for the iterative calculation. For the dynamic systems of structures, the practical formulations of this algorithm are given which can efficiently use the symmetric properties of both the dynamic characteristic matrices of the structures and the solutions of Lyapunov and Riccati equations. Three examples of vibration suppression of large flexible space structures are given to illustrate the application of the algorithm.