Stability regions for multiloop LQ-regulated systems with state estimators

This note 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(\sigma)
are assumed to violate the standard LQ robustness condition
\sigmaN(\sigma) \geq 0.5\sigma^{2}
, either for values of σ away from
\sigma = 0
, or in a neighborhood of
\sigma = 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.