Abstract: In this paper, we consider the vibration controllable system where A ∈ R2n×2n,B ∈ R2n×m and X ∈ R2n×1, U ∈ Rm×1,, are the state and input of the above system. If we usestate feedback, that is, if we set U = FX, in which F ∈E Rp×2n, then we haveX = (A + BF)XFrom the control theory we know that if the system is controllable, then for any given numbersλ1，λ2，……λ2n. there exists a matrix F, such that matrix (A + BF) has eigenvalues λ1,λ2,… λ2n.Robust control is necessary for structures due to the inherent modeli...