Compositional Verification of Passivity for Cascade Interconnected Nonlinear Systems

We consider the problem of verifying passivity of a networked system comprised of dynamically coupled nonlinear subsystems affine in the control input, connected in a cascade architecture. We propose a novel verification approach, wherein the verification is carried out locally at each subsystem using only the dynamics of the particular subsystem and limited information about its coupling with the immediately preceding subsystem in the cascade. The proposed verification is compositional, that is, the addition of new subsystems does not require re-verification of the passivity of the existing network. When a new subsystem is added to the network, only the dynamics of the new subsystem and limited information about its interconnection to the existing network are used to verify passivity of the entire networked system.