Localized stability certificates for spatially distributed systems

We consider a class of spatially distributed linear systems with finite bandwidth. By means of spatial localization techniques, it is shown that exponential stability of this class of systems can be verified in a decentralized and spatially localized fashion, which is practically relevant to many real-world applications. Our proposed necessary and sufficient stability certificates are independent of the dimension of the entire system. Moreover, they only require localized knowledge about the state matrix of the system, which makes these verifiable conditions desirable for design of robust spatially distributed linear systems against subsystem failure and replacement.