  Robust controller synthesis attracts reviving research interest, driven by
the rise of learning-based systems where uncertainty and perturbation are
ubiquitous. Facing an uncertain situation, a robustly stabilizing controller
should maintain stability while operating under a perturbed system deviating
from its nominal specification. There have been numerous results for robust
controller synthesis in multiple forms and with various goals, including
mu-synthesis, robust primal-dual Youla, robust input-output, and robust system
level parameterizations. However, their connections with one another are not
clear, and we lack a general approach to robust controller analysis and
synthesis.
  To serve this purpose, we derive robust stability conditions for general
systems and formulate the general robust controller synthesis problem. The
conditions hinge on the realization-stability lemma, a recent analysis tool
that unifies existing controller synthesis methods. Not only can the conditions
infer a wide range of existing robust results, but they also lead to easier
derivations of new ones. Together, we demonstrate the effectiveness of the
conditions and provide a unified approach to robust controller analysis and
synthesis.
