Cross gramian approximation with Laguerre polynomials for model order reduction

Abstract

This paper considers the problem of model order reduction by approximate balanced truncation with Laguerre polynomials approximation of the system cross gramian. The cross gramian contains information both for the reachability of the system as well as for its observability. The main property of the cross gramian for a square symmetric stable linear system is that its square is equal to the product of the reachability and observability gramians and therefore, the absolute values of its eigenvalues are equal to the Hankel singular values. This is the reason to use the cross gramian for computing balancing transformations for model reduction. Laguerre polynomial series representations are used to approximate the cross gramian of the system at infinity. The orthogonal polynomials of Laguerre possess good convergence properties and allow to reduce the computational complexity of the model reduction problem. Numerical experiments are performed confirming the effectiveness of the proposed method.