asymptotic stability

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asymptotic stability

[ā‚sim′täd·ik stə′bil·əd·ē]
(mathematics)
The property of a vector differential equation which satisfies the conditions that (1) whenever the magnitude of the initial condition is sufficiently small, small perturbations in the initial condition produce small perturbations in the solution; and (2) there is a domain of attraction such that whenever the initial condition belongs to this domain the solution approaches zero at large times.
References in periodicals archive ?
Theorem 2 can be derived from the above analysis: if suppose assumption 1) and 2) set up, then nonlinear neural network (6) exists the only balance point which is globally asymptotically stable.
The simplest performance specification is that of stability: in the absence of any disturbances, we would like the equilibrium point of the system to be asymptotically stable.
a] (corresponding to the control u = a) has an asymptotically stable node at ([p.
If condition (4) is satisfied uniformly with respect to the set [OMEGA], solutions of equation (3) are said to be globally asymptotically stable (or uniformly globally attractive).
Lemma 4 (Wo, 2004): Assume that the system (2) is regular and causal, then it is asymptotically stable if and only if given positive definite matrix W, there exists a positive semi-definite matrix V which satisfies
LTI-TDS is asymptotically stable if all poles are located in the open left half plane, [[?
3) is called locally asymptotically stable if it is locally stable, and if there exist [gamma] > 0 such that for all [x.
i] [parallel]z[parallel] in the region G, then the system(7) is asymptotically stable in the region G.
0](t) is not asymptotically stable, since Re [lambda](A(0)) = 0.
1) is globally asymptotically stable under the assumption that the delay h satisfies a certain restriction in [4].
A particular minimal state variable (MSV) solution is E-stable if the MSV fixed point of the differential equation is locally asymptotically stable at that point.