Scalable Input-to-State Stability for Performance Analysis of Large-Scale Networks

This letter investigates networks of interconnected systems and introduces the notion of “scalable input-to-state stability” (sISS). This concept is based on input-to-state stability (ISS) and can be interpreted as an extension of the well-known concept of string stability from simple line graphs to general graphs. It guarantees that the trajectories of all states are bounded at all times independently of the network's size and structure and can hence be regarded as an important performance notion. Further, sufficient conditions are derived to guarantee sISS of homogeneous networks with well-defined interconnection structures. In fact, the conditions depend on local ISS Lyapunov functions but guarantee the global condition of sISS. Hence, a first step is made towards developing suitable extensions of string stability to general networks. Two examples are discussed to illustrate the theoretical result.