Stability regions for LQ-regulated systems with state detectors

This paper investigates the closed-loop stability of linear, time-invariant systems controlled by linear-quadratic-Gaussian (LQG) type controllers, when the actuators have nonlinearities. The nonlinearities N(??) are assumed to violate the standard LQ robustness condition: ??N(??) ?? 0.5??2 either for values of ?? away from ?? = 0, or in a neighborhood of ?? = 0. The cases with an exponentially stable state estimator, and an estimator with ultimately bounded estimation error are considered, and expressions are obtained for the regions of attraction and ultimate boundedness.