  The problem of controller reduction has a rich history in control theory.
Yet, many questions remain open. In particular, there exist very few results on
the order reduction of general non-observer based controllers and the
subsequent quantification of the closed-loop performance. Recent developments
in model-free policy optimization for Linear Quadratic Gaussian (LQG) control
have highlighted the importance of this question. In this paper, we first
propose a new set of sufficient conditions ensuring that a perturbed controller
remains internally stabilizing. Based on this result, we illustrate how to
perform order reduction of general non-observer based controllers using
balanced truncation and modal truncation. We also provide explicit bounds on
the LQG performance of the reduced-order controller. Furthermore, for
single-input-single-output (SISO) systems, we introduce a new controller
reduction technique by truncating unstable modes. We illustrate our theoretical
results with numerical simulations. Our results will serve as valuable tools to
design direct policy search algorithms for control problems with partial
observations.
