Robustness Analysis of Exponential Stability of Neutral-Type Nonlinear Systems With Multi-Interference

Abstract

With a view to the unfavorable impact of the inevitable exogenous interferences for the practical engineering and signal transmission, here we focus on the robustness of global exponential stability for nonlinear dynamical system subject to piecewise constant arguments, neutral terms and stochastic disturbances (SNPNDS). A new troublesome problem is that the neutral terms appeared in the derivative part affected on the other two interference factors is not a simple accumulation, so the Lipchitz condition is adopted to establish the ternary transcendental equations. However, different from previous transcendental equations with single or double variables, solving the transcendental equations with three variables becomes the bottleneck again. Hence, the special independent parameters & interdependent variables method targeted for SNPNDS is adopted here: firstly, all relative independent parameters are fixed. Next, the upper bounds of these three interdependent variables are orderly derived by their coupling relationship. Therein, the optimal constraint conditions for piecewise constant arguments and neutral terms are deduced. Through the strategies mentioned above, a class of algebraic problems of estimating three upper bounds by solving transcendental equations with three variables is settled. Besides, the main method ensures the relationship built among the interference factors is mutually restrictive and dynamic. Meanwhile, the optimized constraints make the linkage effect more comprehensive and valid. Furthermore, the established mechanism is practical enough to be generalized to more multivariable systems. Finally, the numerical simulation comparisons are given to illustrate the validity of the derived results.INDEX TERMS Robustness, nonlinear system, neutral term, piecewise constant argument, stochastic disturbance.

Robustness Analysis of Fuzzy Cellular Neural Network With Deviating Argument and Stochastic Disturbances

“…In addition, stability as a prerequisite for the application of the neural networks with deviating arguments, it has been widely studied, see, [24], [25], [26], [27], [28], [29]. Furthermore, the length of the deviating interval also affects the stability of a dynamical system, in [30] and [31], Zhang and Si further studied the robustness of exponential stability of nonlinear system with deviating argument on the basis of the result of stability. And they estimate the upper bound of the interval length of deviating function.…”

Robustness Analysis of BAM Cellular Neural Network with Deviating Arguments of Generalized Type

“…Robustness is the ability of a control system to maintain a specifc level of performance when certain parameters are perturbed, and it is of great signifcance for the design and application of system. As for the analysis of RoS, there are lots of interesting outcomes, such as, Si et al further studied RoS of dynamical systems with deviating arguments in [26][27][28]; Fang et al analyzed the RoS of fuzzy CNN with deviating argument in [29]. In [30], RoS of recurrent neural network is investigated.…”

Robustness analysis of exponential stability of fuzzy inertial neural networks

“…This is also a motivation for this article. At present, most researches on ROS only focuses on first-order neural networks [26,27,[32][33][34][35][36]. However, in practical applications, due to the inherent special properties of electronic components, high-order neural network models are usually needed to more accurately describe their dynamic behaviors in reality.…”

“…Compared with [14,15], the ROM used in this paper includes two positive variable parameters η i , ξ i , which further expands the ROM used in [14,15] which is only contain one variable parameter. • In addition, in this paper, we have removed the limitation on the derivative of time delay function ς(t) in [33][34][35][36]39], which means that ς ′ (t) ≤ δ < 1 not satisfied in this paper. • The upper limits of time delay and max intensity of noise are obtained respectively by applying Grownwall-Bellman lemma as well as inequality techniques to ensure the perturbed FINNs keep exponential stability.…”