Non-Linear Networked Systems Analysis and Synthesis using Dissipativity Theory

We consider networked systems comprised of interconnected sets of non-linear subsystems and develop linear matrix inequality (LMI) techniques for their analysis and interconnection topology synthesis using only the dissipativity properties of the involved subsystems. In particular, we consider four networked system configurations (NSCs) and show that the analysis of their stability/dissipativity can be formulated as corresponding LMI problems. Using some matrix identities and mild assumptions, we also show that the synthesis of interconnection typologies for these NSCs can also be formulated as LMI problems. This enables synthesizing the interconnection topology among subsystems to enforce/optimize specific stability/dissipativity properties over the networked system. The formulated LMI problems can be solved efficiently and scalably using standard convex optimization toolboxes. We also provide several numerical examples to illustrate our theoretical results.