  In these notes we collect some results from several of the authors' works in
order to make available a single source and show how the approximate geometric
methods for regulation have been developed, and how the control design strategy
has evolved from the theoretical methods, involving the regulator equations, to
what we now call the regularized controller. In between these two extremes we
developed, in a series of works, a fairly rigorous analysis of the
regularization scheme leading to the regularized dynamic regulator equations
and an iterative scheme that produces very accurate tracking and disturbance
rejection control laws. In our most recent work we have extended dynamic
regulator equations to what we now refer to as the regularized controller. This
new formulation has only recently being applied to examples including linear
and nonlinear delay equations.
