MATHEMATICAL ENGINEERING TECHNICAL REPORTS H2 and H∞ Norm Computations for LTI Systems with Generalized Frequency Variables

A class of large-scale systems with decentralized information structures such as multi-agent dynamical systems can be represented by a linear system with a generalized frequency variable. In this paper, we propose efficient H2 and H∞ norm computations based on the generalized frequency variable. Specifically, we first derive a way of H2 norm computation from state-space realizations of subsystems. We then discuss a region on the complex plane specified by the generalized frequency variable for achieving the H∞ norm bound for a simple feedback case, and a graphical test and three different numerical methods for computing the H∞ norm are derived. The last part is devoted to the loop shaping type H∞ norm, where a graphical test for the condition and three different ways of computing the H∞ norm are provided.