A linear quadratic regulator (LQR) for mechanical vibration systems is studied based on second-order matrix equations. The performance index is a functional depending on second derivatives. The Euler-Lagrange equations lead to linear second-order system matrix-augmented differential equations whose stable eigenvalues are the poles of the closed-loop optimal controlled systems. The optimal feedback constant matrices are determined by the stable eigenpairs, the control input matrix and the control weight matrix. The traditional matrix Riccati equ...
