Solving a robust stability optimisation problem via optimal model reduction: a parameterised approach

The design of control systems based on a plant often requires complex computations if the plant to be controlled is of a high order or is unknown. An accepted approach to this problem is to design a control system based on an approximate plant. It is necessary that the control system not only stabilises the approximate plant but also a family of systems which exist in an uncertainty region around this plant. A new optimal model reduction method to derive an approximate model is presented in this paper. The method involves optimising a "small-gain" type sufficient condition and results in an optimal approximate plant as well as a robust control system. For a suitable transformation on a template approximate open-loop system the optimisation problem for model selection reduces to a standard optimal model reduction problem.