On the performance of different capability indices under normal and non-normal distributions

In this article, we have examined the performance of some useful capability indices using normal and non-normal distributions. The confidence intervals are calculated and mean coverage rates are observed for different capability indices. The effects of symmetry and kurtosis of parent distributions are examined on the mean coverage rates of different capability indices. Moreover, we have investigated the robustness (of confidence interval) using the median and percentile-based indices. We have considered the well-known distributions including normal, gamma, t, Weibull, and chi-squared. For these process scenarios, we have observed that some indices resist disturbance only in symmetry of the parent distribution, some resist the disturbance in symmetry and kurtosis of the distribution, and some indices don’t resist against either type of disturbance.     

Stability and boundedness in difference systems with finite delay

In this paper, stability and boundedness theorems for delay difference systems with the condition

δV(n,x(n))≤-W₂(|x(n)|)+σ

are given, where Δ is the backward difference operator. Some known results are generalized.     

二阶中立型时滞微分方程非振动解的渐近性

在本文中,讨论了一类非线性中立型时滞微分方程非振动解的渐近性,扩充并改进了已有结果．     

一种最大向量平均个数的估计方法

提出一种估计n个d维向量中最大向量平均个数的方法。该方法通过分析单个向量与其他向量子集的支配关系,求出最大向量平均个数的解析式。证明解析式满足已知的递归关系,得到最大向量平均个数的近似估计。与已有方法相比,该方法可应用到估计k个其他向量支配的平均个数问题。     

Global stability analysis scheme for a class of nonlinear time delay systems

We consider a class of nonlinear time delay systems created by generalizing the model for FAST TCP, an Internet congestion control algorithm. We achieve a time delay independent sufficient condition for the global asymptotic stability of the class of systems. The sufficient condition is verified by constructing two sequences that represent the lower and upper bound variations of the system trajectory in time, and showing that the two sequences converge to the equilibrium point of the system. The simulation results exemplify that the sufficient condition is valid for global asymptotic stability, and that the sufficient condition is a close approximation to the unknown necessary and sufficient condition for global asymptotic stability.     

Geometrically non-linear behavior of structural systems with random material property: An asymptotic spectral stochastic approach

An asymptotic spectral stochastic approach is presented for computing the statistics of the equilibrium path in the post-bifurcation regime for structural systems with random material properties. The approach combines numerical implementation of Koiter’s asymptotic theory with a stochastic Galerkin scheme and collocation in stochastic space to quantify uncertainties in the parametric representation of the load–displacement relationship, specifically in the form of uncertain post-buckling slope, post-buckling curvature, and a family of stochastic displacement fields. Using the proposed method, post-buckling response statistics for two plane frames are obtained and shown to be in close agreement with those obtained from Monte Carlo simulation, provided a fine enough spectral representation is used to model the variability in the random dimension.     

On the analysis of nonlinear nilpotent switched systems using the Hall–Sussmann system

We consider an open problem on the stability of nonlinear nilpotent switched systems posed by Daniel Liberzon. Partial solutions to this problem were obtained as corollaries of global nice reachability results for nilpotent control systems. The global structure is crucial in establishing stability. We show that a nice reachability analysis may be reduced to the reachability analysis of a specific canonical system, the nilpotent Hall–Sussmann system. Furthermore, local nice reachability properties for this specific system imply global nice reachability for general nilpotent systems. We derive several new results revealing the elegant Lie-algebraic structure of the nilpotent Hall–Sussmann system.     

New LMT-based delay-dependent criterion for global asymptotic stability of cellular neural networks

The problem of global asymptotic stability analysis is studied for a class of cellular neural networks with time-varying delay. By defining a Lyapunov–Krasovskii functional, a new delay-dependent stability condition is derived in terms of linear matrix inequalities. The obtained criterion is less conservative than some previous literature because free-weighting matrix method and the Jensen integral inequality are considered. Three illustrative examples are given to demonstrate the effectiveness of the proposed results.     

Global asymptotic stability of delayed neural networks with discontinuous neuron activations

This paper investigates a class of delayed neural networks whose neuron activations are modeled by discontinuous functions. By utilizing the Leray–Schauder fixed point theorem of multivalued version, the properties of M-matrix and generalized Lyapunov approach, we present some sufficient conditions to ensure the existence and global asymptotic stability of the state equilibrium point. Furthermore, the global convergence of the output solutions are also discussed. The assumptive conditions imposed on activation functions are allowed to be unbounded and nonmonotonic, which are less restrictive than previews works on the discontinuous or continuous neural networks. Hence, we improve and extend some existing results of other researchers. Finally, one numerical example is given to illustrate the effectiveness of the criteria proposed in this paper.     

Conditions for local almost sure asymptotic stability

In this paper, we investigate local asymptotic stability ensured by the addition of Gaussian white noise into dynamical systems. There are different stability notions for stochastic systems, such as asymptotic stability in probability (ASiP) and uniform almost sure asymptotic stability (UASAS). The local ASiP property is incapable of ensuring that sample paths converge to the origin with probability one, whereas the local UASAS property is capable of it. However, in general, the local UASAS property requires tight conditions. Here, we provide our notion of local almost sure asymptotic stability (local ASAS) to relax the conditions with both almost sure convergence of sample paths to the origin and the existence of bounded (weak) invariant sets. We find that the addition of Gaussian white noise always prevents the origin from being locally UASAS as long as we consider smooth Lyapunov functions; however, it is possible to make the origin locally ASAS. The result is confirmed by a simple example of elimination of unstable equilibria by deliberately adding Gaussian white noise.