Some reflections on the current theory of robust control

The purpose of this article is to make a critical analysis of the so-called robust control theory, from an input-output perspective. Viewing a system as a function that maps excitations into responses, it argues that while deviations in the graph of the function are usually accounted for in robust control theory, restrictions in the domain of definition of the function are usually ignored. The claim is made that these restrictions are necessary for the theory to be significant. A reformulation of the classical theory of input/output systems is proposed, based on the concept of binormed extended space, previously introduced by the author in [1]. The results mark a clear separation between local and global notions of input-output stability, much in the spirit of the notions of local and global stability in the sense of Lyapunov.