Least-squares parameter set estimation for robust control design

Two least-squares based methods are presented for obtaining ARX model sets. The first is obtained using properties of high-order ARX models and the second uses a stochastic embedding scheme on the residuals from an ARX model of any order. Either of the ARX model sets is useful for robust control of systems with uncertain parameters. Using the high order ARX model approach, the parameter uncertainty lies in a confidence ellipsoid. Using the stochastic embedding approach, the parameter uncertainty is in a confidence box. For scalar plants, both cases can be handled using convex programming to obtain the exact stability robustness margin for a particular controller. However, because the uncertainty description is probabilistic, the robustness property has to be associated with a confidence level, i.e., a probability of stability.