Optimal H² model reduction for mechanical systems

The H2 optimal model reduction problem, is addressed, to obtain reduced, order models for mechanical systems described, by matrix second, order linear systems such that the H2 norm, of the error system, is minimized. The structure of the original second, order model is preserved, in the model reduction procedure and, the reduced, order models are guaranteed, to be stable. The expression of the error and, its gradient are explicitly given in terms of the solutions of certain Lyapunov equations. An effective algorithm, is derived, to obtain the reduced, order model. Two numerical examples are provided to illustrate the effectiveness of the proposed method.