D-K iteration with optimal scales for systems with time-varying and time-invariant uncertainties

A D-K iteration algorithm is presented that allows for both time-invariant and time-varying uncertainties and parameters to be accounted for during synthesis. The procedure developed in this paper incorporates a recent extension of robustness analysis that provides optimal D-scales for systems having these mixed uncertainties and parameters. Utilizing these optimal scales allows the systems dependence on parameter variations and uncertainties to be modeled more precisely. Accurately representing uncertainty during synthesis results in less conservative controllers that are more robust to the true system variations. The procedure is demonstrated by designing a linear parameter-varying (LPV) pitch-rate controller for the F-16 Variable Stability In-Flight Simulator Test Aircraft modeled as an LPV system with time-varying parameters and time-invariant uncertainties. This design shows that using optimal scales results in less conservative results.