Stochastic finite-time boundedness for Markovian jumping neural networks with time-varying delays

Exponential stability criterion for interval neural networks with discrete and distributed delays

“…It should be noted that, in Theorem 3.3, the exponential convergence rate index k is the unique positive solution of the equation k ¼ k 1 À k 2 e ks . The obtained exponential convergence rate index k is determined by the time delay s because of the condition (34). In other words, the condition obtained in Theorem 3.3 is delay-dependent.…”

Non-fragile finite-timel2−l∞state estimation for discrete-time Markov jump neural networks with unreliable communication links

“…This is one of our motivations to do this work. What's more, distinguished from classical stability concept, finite-time stability is mainly focused on the asymptotic behavior of the system over a finite time interval, which can be used to address the transient performances of control systems [1,4,18]. However, to the best of our knowledge, the problem of finite-time NFSE has not been fully researched, which further motivates our current investigation.…”

“…In this paper, the measurement output collected by the sensor from the plant is shown as follows: (4) where y(k) = C i x(k) ∈ R m is the expected measurement output of the plant where C i are real constant matrices with appropriate dimensions for all η(k) = i ∈ S; y d (k) = C di x(k − d(k)) is the retarded measurement output of the plant; d(k) is a differential function representing the time-varying delay and satisfies 0 < d(k) ≤ h, where h is a constant positive scalar. ϕ(y(k)) stands for the sensor nonlinearity of the system.…”

Stochastic finite-time boundedness on switching dynamics Markovian jump linear systems with saturated and stochastic nonlinearities

“…For all these reasons, it is not trivial to explore the dynamic behaviors of SD-MJLS over a fixed finite-time interval. The original concept of finite-time control and the finite-time control problems for common MJLSs could be reviewed in [1,2,10,11,16,17,32,38,39,40,42,43,44]. For a SD-MJLS, the controller design approaches available rely on the ideal assumption that the control move and the measurement signal can be obtained with unlimited amplitudes.…”