Input-output analysis of distributed parameter systems using convex optimization

This paper investigates input-output properties of systems described by partial differential equations (PDEs). Analogous to systems described by ordinary differential equations (ODEs), dissipation inequalities are used to establish input-output properties for PDE systems. Dissipation inequalities pertaining to passivity, induced L²-norm, reachability, and input-to-state stability (ISS) are formulated. For PDE systems with polynomial data, the dissipation inequalities are solved via polynomial optimization. The results are illustrated with an example.