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
Therefore, whole closed-loop system is asymptotically stable
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 .
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.