Controller reduction via stable factorization and balancing

A controller reduction procedure based on a representation of a controller as a matrix function defined using stable proper transfer functions and employing a balancing technique is studied in this paper. For a certain right coprime factorization of an LQG designed controller K(s) = N(s)D^-1(s), we approximate using a balancing technique the pair [D(s), N(s)]^T by a low-order pair [D₁(s), N₁(s)]^T defining a factorization of the reduced-order controller K₁(s) = N₁(s)D₁^-1(s). We show that reducing the controller order in this way is motivated in a natural way, which leads to the expectation of both good stability properties and good accuracy of approximation of closed-loop behaviour. This is also demonstrated in some examples.