A method for estimating upper and lower bounds of eigenvalues of closed-loop systems with uncertain parameters

Using the convex model theory, the vibration control problem of structures with uncertain parameters is discussed, which is approximated by a deterministic one. A method for estimating the upper and lower bounds of eigenvalues of the closed-loop systems is presented by combining the matrix perturbation and optimization. The present method is applied to a vibration system to illustrate the application. The numerical results show that the present method is effective.