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, i.

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.