Abstract
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.
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