Stability of multiloop LQ regulators with nonlinearities--Part I: Regions of attraction

The closed-loop stability of linear, time-invariant systems controlled by linear quadratic (LQ) regulators is investigated when there are nonlinearities in the control channels which lie outside the (
0.5, \infty
) stability sector in regions away from the origin (i.e., saturation-type nonlinearities). An estimate of the region of attraction is obtained which provides methods for selecting the performance function weights for more robust LQ designs.