LMI stability condition for linear systems with generalized frequency variables

A class of large-scale systems with decentralized information structures such as multi-agent systems can be represented by a linear system with a generalized frequency variable. In this paper, we investigate stability of such systems, which is the most fundamental property from the view point of control. Specifically, we first present a systematic way of deriving a Hurwitz type stability criterion and then show that it can be reduced to a linear matrix inequality (LMI) feasibility problem involving generalized Lyapunov inequalities. Furthermore, the properties of the LMI stability condition are examined, and they are confirmed by numerical examples.