Estimation of Regions of Attraction and Ultimate Boundedness for Multiloop LQ Regulators

The closed-loop stability of linear, time-invariant systems controlled by linear quadratic (LQ) regulators is investigated when there are nonlinearities N(¿) in the control channels which violate the condition: ¿ N(¿) ¿ 0.5¿² (i.e., the condition that gains ¿ ¿), either for values of ¿ away from ¿=0, or in a neighborhood of ¿=0. Expressions are obtained for the regions of attraction and ultimate boundedness for these cases, which provide methods for selecting the performance function weights to obtain more robust LQ designs.