Objective: Study of infinite dimensional systems, modeled by partial differential equations (PDEs), connected through boundary conditions to finite dimensional systems, modeled by ordinary differential equations (ODEs). Motivation: Allows modeling many physical phenomena, including transport processes, and interaction between heat diffusion and chemical reactions, with ODEs acting as sensors, controllers, and actuators. Limited research on the robust input-output approach for these systems. Innovative Aspects: - Robust control-like modeling of such heterogeneous systems, moving towards multi-dimensional space and multi-variable input-output systems. - Methodological tools like IQC or a new type of separator to produce numerically efficient analysis results for heterogeneous systems. - Methods for the synthesis of controllers or observers within the chosen formalism.