Compositional Analysis of Interconnected Systems Using Delta Dissipativity

This letter extends the notion of delta dissipativity, originally introduced in a game theoretic context, to general interconnections of dynamical systems. The main contribution of this letter is a compositionality result that presents conditions under which a large-scale interconnection of delta dissipative systems is delta dissipative. We adapt this result to also analyze stability and asymptotic stability of equilibrium points for the interconnection. Additionally, we formulate a sum-of-squares program for verifying delta dissipativity of a (polynomial) system. The results are illustrated with examples.