Stability Analysis of Spatially Invariant Interconnected Systems with Networked Communication

In this paper tractable stability conditions are presented for a system consisting of an infinite number of spatially invariant subsystems interconnected through communication networks. The networks transmit packets asynchronously and independently of each other and are equipped with scheduling protocols that determine which actuator, sensor or controller node is allowed access to the network. The overall system is modeled as an interconnection of an infinite number of spatially invariant hybrid subsystems. Based on this framework, conditions leading to a maximally allowable transmission interval (MATI) for all of the individual communication networks is derived such that uniform global asymptotic stability (UGAS) of the overall system is guaranteed. These conditions only involve the local dynamics of a single hybrid subsystem in the interconnection. In the case of linear subsystems the conditions can be stated in terms of linear matrix inequalities thereby making them numerically tractable. An illustrative example of a platoon of vehicles is used to demonstrate the newly obtained results and their applications.