Input-Output Control of Composite Systems

Composite systems are large-scale plants composed of multiple individual units. We apply classical input-output techniques to controller design problems for such composite systems. Before being able to apply these techniques, the core issue is to establish a quadratic inequality on the composite input-output tuples, given only distinct quadratic inequalities on the individual input-output tuples of the entities constituting the composite system. Having established a technique to derive such quadratic inequalities, we apply the feedback theorem for conic relations, the small-gain theorem, and the feedback theorem for passive systems to our class of composite systems. Our results connect to the internal model principle, the S-procedure, and the simultaneous stabilization problem.