Performance-preserving frequency weighted controller approximation: a coprime factorisation approach

Given a stabilising controller which satisfies a prespecified H _∞ performance bound on the closed loop, we derive sufficient conditions for reduced order controllers to be stabilising and satisfy the same performance bound. The conditions are expressed as norm bounds on the frequency weighted error between coprime factor representations of the given controller and the reduced order controller. Reduced order controllers are then designed by interpreting the sufficient conditions as frequency weighted model reduction problems