On the Design of Robust LQ Regulators

Sufficient conditions are obtained for global asymptotic stability of linear systems controlled by linear quadratic (LQ) regulators when nonlinearities or unmodeled linear dynamics are present in the loop. The conditions are less conservative than the standard LQ robustness results because they generally yield phase margins ≫ 60°, and tolerance to nonlinearities having gains ≪ 1/2. The conditions also provide a measure of robustness of a given LQ design to unmodeled dynamics and nonlinearities. For open-loop stable plants, it is proved that a class of LQ regulators can always be designed to have ±90° phase margin and tolerance to nonlinearities in the ([0, ¿) sector.