Stability of multiloop LQ regulators with nonlinearities--Part II: Regions of ultimate boundedness

This note investigates the closed-loop stability of linear time-invariant systems controlled by linear quadratic (LQ) regulators when there are nonlinearities in the loops which escape the (
0.5, \infty
) stability sector in a bounded region containing the origin. An estimate of the region of ultimate boundedness is obtained, which provides methods for selecting the performance function weights to get better regulator designs.