On the Directional Dependence and Null Space Freedom in Uncertainty Bound Identification

In previous work, the determination of uncertainty models via minimum norm model validation is based on a single set of input and output measurement data. Since uncertainty bounds at each frequency is directionally dependent for multivariable systems, this will lead to optimistic uncertainty levels. In addition, the design freedom in the uncertainty model has not been utilized to further reduce uncertainty levels. The above issues are addressed by formulating a minmax problem. An analytical solution to the min-max problem is given to within a generalized eigenvalue problem, thus avoiding a direct numerical approach. This result will lead to less conservative and more realistic uncertainty models for use in robust control.