Parametric control of conservative mechanical systems

Parametric excitation is used to control the vibration of a conservative mechanical system. The excitation is varied according to a quadratic, state feedback, control law. If the system has distinct eigenvalues and a full rank, diagonalizable, parametric control matrix, then the control law is asymptotically stabilizing. To eliminate the required full state sensing, an observer is designed to estimate the states from the minimum number of linear measurements. There always exists an observer if the system is linearly observable and the control is bounded. An example demonstrates the method.