Abstract
A class of large-scale networked dynamical systems with decentralized information structures such as multi-agent dynamical systems can be represented by an LTI system with a generalized frequency variable. This paper summarizes recent results on the fundamental analysis, namely stability conditions, \({\mathcal H}_{2}\)-norm computations, and \({\mathcal H}_{\infty}\)-norm conditions, for LTI systems with generalized frequency variables. We also show an analytic condition for the existence of protein level’s periodic oscillations in cyclic gene regulatory networks as an application.
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