Two upper bounds on the H∞-norm of LTI dynamical systems

Abstract: The poles/residues expression of the frequency-limited H2-norm is used to derive two upper bounds on the H∞-norm of a MIMO LTI dynamical system. These bounds can be efficiently computed when the eigenvalues and eigenvectors of the model are available. This specificity make them particularly well suited to watch the H∞-norm of the approximation error in the context of the frequency-limited H2 model approximation method suggested recently by the authors.The efficiency of these bounds, as well as their integration in the model approximation algorithm are illustrated through several numerical examples