Robustness Margins for Linear Parameter Varying Systems

An approach for extending classical robustness margins to linear parameter varying (LPV) systems is presented. LPV systems are often used to model aircraft dynamics that are highly dependent on the operating conditions such as altitude and airspeed. Classical gain and phase margins are evaluated in the frequency domain and therefore cannot be applied to LPV systems. The proposed approach is based on a time-domain interpretation for disk margins. Specifically, a norm bounded linear time invariant (LTI) uncertainty is interconnected to the nominal LPV system.
Next, a time-domain worst-case metric is applied to evaluate both the robustness margin and also the robust performance degradation. The approach does not require detailed uncertainty modeling. In addition, the analysis can be formulated as a convex optimization leading to reliable numerical analysis tools. As an example, the LPV gain margin of a flutter suppression controller for a flexible aircraft is evaluated.