Summary: Complexity and Fragility in Stability for Linear Systems
Aaron D. Ames and John C. Doyle
Abstract-- This paper presents a formal axiomization of the
notion that (proof) complexity implies (property) fragility and
illustrates this framework in the context of the stability of both
discrete-time and continuous-time linear systems.
Understanding the robustness of systems with respect
to a certain property plays a fundamental role in design
and analysis; when systems are robust they tend to behave
properly in both foreseen and unforseen circumstances. It
is, moreover, often the case that the lack of robustness, or
fragility, of a system is indicated when trying to prove that
the system has a certain property. That is, that the complexity
of a proof relates directly to--and in fact implies--the
fragility of the property being proven. Yet this connection
has, for the most part, remained anecdotal.
Taking the idea that complexity implies fragility beyond
the anecdotal level has important practical consequences.
On a general level, when using automated proof techniques