Enhanced result on stability analysis of randomly occurring uncertain parameters, leakage, and impulsive BAM neural networks with time‐varying delays: Discrete‐time case

Abstract

In real-world problems, neural networks play an increasingly important role in terms of both theory and applications. In this paper, the asymptotic stability analysis issue is investigated for uncertain impulsive discrete-time bidirectional associative memory neural networks with leakage and time-varying delays. With the assistance of novel summation inequality, reciprocally convex combination technique, and triple Lyapunov-Krasovskii functionals terms, many cases of time-varying delays are examined to certify the stability of neural networks. Here, the uncertainties are considered as a randomly occurring parameter uncertainty, and it conforms certain mutually uncorrelated Bernoulli-distributed white noise sequences. An important feature of the results reported here is that the probability of occurrence of the parameter uncertainties specify a priori estimate. Finally, numerical examples are proposed to expose the capability and efficiency of our research work with the help of the LMI control toolbox in MATLAB.

Event-based robust stabilization for delayed systems with parameter uncertainties and exogenous disturbances

“…The RISpS property means that state of the closed-loop system (7) will eventually enter the set B(0, γ c (|v| ∞ ) + d c ) bounded by the threshold parameter ξ 2 and the exogenous disturbance |v| ∞ . This dynamical performance is quite different from and more general than the asymptotical stability [6,14], robust stability [16][17][18][19][20][21][22][23][24][25][26][27], and the conventional ISS [10,12,13]. Furthermore, from the point of view of technique analysis, we adopt the Lyapunov function method for the dynamics of state x(t) while the impulsive jumping estimation method for the control input u(t k ) at event-triggering instants, which shows some hybrid characteristics and is quite different from the common L-K functional approach used in [16-18, 21-27, 48].…”

“…When all uncertainties are removed, Definition 1 reduces to the conventional ISS concept introduced in [11,12,34] and the term γ c (|v| ∞ ) + d c is used to represent the bound of the domain where the state remains. When d c = 0 and v(t) ≡ 0, Definition 1 reduces to the asymptotically robust stability considered in [20][21][22][24][25][26] and the KL-function β c indicates that the state will tend to zero as t → +∞ for all admissible parameter uncertainties satisfying (2).…”

“…If (25) does not hold, then there exists some t > 0 such that U * (t) > U(t). By denoting t * := inf t {t > 0 : U * (t) > U(t)}, it is derived from the continuity of U * (t) and U(t) that…”

“…Hence the uncertain parameters of a system are only due to the deviations and perturbations of its parameters. Recently, significant progress has been made in the study of robust stability and controller synthesis for delayed systems with parameter uncertainties [16][17][18][19][20][21][22][23][24][25][26][27]. For example, in [17], the robust stability has been studied for a class of linear networked control systems with dynamic quantization, variable sampling intervals as well as communication delays.…”

“…(1) The RISpS property is, for the first time, proposed to evaluate the dynamical behaviors for a class of uncertain delayed systems with disturbances, which is quite different from and more comprehensive than the ISS properties investigated in [7-10, 12, 13, 15, 34-36] and the robust stability studied in [16][17][18][19][20][21][22][23][24][25][26][27]. (2) Several previous literature such as [1,3,6,11,23,27] required that the control signal updates continuously with time, which may lead to the unnecessary cost of network resources.…”