asymptotic expansion

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asymptotic expansion

[ā‚sim′täd·ik ik′span·shən]
(mathematics)
A series of the form a0+ (a1/ x) + (a2/ x 2) + · · · + (an / xn) + · · · is an asymptotic expansion of the function f (x) if there exists a number N such that for all nN the quantity xn [f (x) -Sn (x)] approaches zero as x approaches infinity, where Sn (x) is the sum of the first n terms in the series. Also known as asymptotic series.
References in periodicals archive ?
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].