Practical set invariance for decentralized discrete time systems

This paper discusses set invariance notions for decentralized discrete time systems which are physically inter-connected. We employ independent set-dynamics induced by the underlying subsystems subject to the available information in the decentralized setting. The main novelty of the approach lies within the fact that the concept of set invariance for independent set-dynamics is formalized by employing appropriate families of sets. The complexity of the exact notion is alleviated by introducing a practical set invariance notion which is then complemented with the corresponding relaxed stability analysis. Under mild assumptions, the introduced notion allows for safe, stable and independent operation of the subsystems forming the overall decentralized system.