Actually, the nonlinear separation principle is available, according to the Lyapunov stability theorem, when observer errors themselves are asymptotically convergent
, and their transition processes do not destabilize the systems controlled by estimated-states feedback controllers.
Theorems 2, 5, 8, and 11 show that if the inequality signs are strict, then, for any initial [x.sub.0] whether it is in feasible set [OMEGA] or not, the state vectors are exponentially or asymptotically convergent
. When the inequality signs are not strict, Theorem 15 shows that the sufficient condition ensuring system being asymptotically stable is [x.sub.0] [member of] [OMEGA].
is asymptotically convergent to the slowly varying disturbance when the nonlinear weighted function
is asymptotically convergent to the slope forms disturbance when the initial nonlinear weighted function [g.sub.0](e) has the same form as Theorem 2 and the coefficients [sigma],w, and[T.sub.0] are properly selected according to [[LAMBDA].sub.0] and [[LAMBDA].sub.1].