⎯The problem of the global exponential stability of a class of Hopfield neural networks is considered. Based on nonnegative matrix theory, a sufficient condition for the existence, uniqueness and global exponential stability of the equilibrium point is presented. And the upper bound for the degree of exponential stability is given. Moreover, a simulation is given to show the effectiveness of th...

We study the relationship between global exponential stability of an invariant manifold and existence a positive semidefinite Riemannian metric which is contracted by flow. In particular, we investigate how following properties are related to each other (in case): 1) A globally “transversally” exponentially stable; 2) corresponding variational system admits same property; 3) there exists degene...

and Applied Analysis 3 (S2) (h 0 , h)-globally exponentially stable, if there exist constants α > 0 and C ⩾ 1 such that, for all ξ ∈ PC b F t0 ([−τ, 0];Rn) and t 0 ∈ R + , Eh (t, x (t; t 0 , ξ)) ⩽ CEh 0 (t 0 , ξ) e−α(t−t0), t ⩾ t 0 . (6) Remark 4. The (h 0 , h)-stability notions are considered here in the spirit of the work by Lakshmikantham and Liu [26] to unify different stability concepts fo...

We study the a.s. exponential stability of the optimal lter w.r.t. its initial conditions. A bound is provided on the exponential rate (equivalently, on the memory length of the lter) for a general setting both in discrete and in continuous time, in terms of Birkhoo's contraction coeecient. Criteria for exponential stability and explicit bounds on the rate are given in the speciic cases of a di...

The uniform random number can be manipulated to simulate the characteristics of any probability density function. For power system reliability analysis the exponential and the Weibull distributions are well suited. Simulated exponential and Weibull random variables can be obtained from uniform (0,1) RNs by making use of the fact that the cumulative density function (CDF) is uniform between zero...

Stability is a general notion that quantifies the sensitivity of a learning algorithm’s output to small change in the training dataset (e.g. deletion or replacement of a single training sample). Such conditions have recently been shown to be more powerful to characterize learnability in the general learning setting under i.i.d. samples where uniform convergence is not necessary for learnability...