Packet-based (wireless) communication networks offer various advantages over dedicated point-to-point wired links in (motion) control systems. These advantages include, most importantly, larger flexibility, ease of reconfigurability, and a decrease in the installation costs, however, only at the cost of decreased reliability as a result of possible packet-losses, varying transmission intervals, varying transmission delays, and the presence of a scheduling protocol. Moreover, the usage of such communication networks will introduce quantization errors. To overcome these problems, stability and performance of networked control systems (NCSs), the class of control systems where the control-loop is closed over a shared network, have extensively been investigated. By using the hybrid modeling framework of a jump-flow system to model such a NCS and by using Lyapunov-based arguments for stability and performance, tractable conditions have been derived leading to bounds on the transmission interval such that uniform global asymptotic stability (UGAS) or Lp-stability for the NCS is guaranteed. In addition, as many control systems consist of interconnections of subsystems, stability and performance have also been analyzed for a finite number of interconnected NCSs. However, when using the obtained analyzing tools in these works, severe limitations will be quickly encountered as they cannot handle systems of very high or even infinite dimension. In this study, this particular problem is taken into consideration by studying a general setup consisting of an infinite number of spatially invariant interconnected subsystems that use packet-based communication networks for the exchange of information between the plants and/or controllers. Inspired by the research line on NCSs, the overall system is modeled as an interconnection of spatially invariant hybrid systems. However, as this overall system is infinite dimensional, a new notion of solutions has to be introduced as the standard solution concepts for hybrid systems do not apply since Zeno behavior (an infinite number of actions in a finite time interval) is inevitable. By using Lyapunov-based arguments, conditions are derived such that UGAS or Lp-stability is guaranteed. Moreover, it will be shown that these conditions are local in the sense that they only involve the dynamics of one subsystem and the information of the local network. In addition, when the flow equations of the spatially invariant (hybrid) subsystems are governed by linear dynamical equations, these conditions for stability and performance can even be stated in terms of linear matrix inequalities (LMIs). Besides studying the infinite interconnection of networked systems, a second line of research focuses on the finite interconnection of NCSs which are not necessarily spatially invariant. As each individual network corresponding to a NCS can either operate in a time-triggered way or an event-triggered way, by using a small-gain approach novel stability conditions are derived in the case that both NCS variants (time-triggered and event-triggered) are present in the same interconnection. These conditions will lead to bounds on the transmission intervals such that UGAS or Lp-stability is guaranteed for the overall interconnected system. Finally, similar to the infinite interconnection, it is shown that when the linear case is considered that the derived conditions can be stated in terms of LMIs. For both the infinite as well as the finite considered interconnections, numerical examples will be used to illustrate the introduced stability and performance analysis.