Multiplicative approximation of transfer functions with frequency weighting

An algorithm for transfer function order reduction is presented, which generalizes the balanced stochastic truncation algorithm to allow for input weighting. An example illustrates use of the algorithm to secure smaller dB error in selected frequency bands through the introduction of the weighting.     

Sampled-data controller reduction procedure

The problem of controller order reduction aimed at preserving the closed-loop performance of a sampled-data closed-loop system is investigated. Past sampling of the system at a multiple of the sampling frequency followed by lifting allows capturing of the system's intersample behavior and yields a time-invariant single-rate system; this then permits standard order-reduction ideas to be applied. Special weighting functions aimed at preserving the closed-loop transfer function are obtained, and weighted balanced truncation is used to reduce the controller, An example shows that without the use of fast-sampling, an unstable closed loop can result from the reduction