Robust exponential stability of uncertain impulsive stochastic neural networks with delayed impulses

In this paper, by using Lyapunov functions, Razumikhin techniques and stochastic analysis approaches, the robust exponential stability of a class of uncertain impulsive stochastic neural networks with delayed impulses is investigated. The obtained results show that delayed impulses can make contribution to the stability of system. Compared with existing results on related problems, this work improves and complements ones from some works. Two examples are discussed to illustrate the effectiveness and the advantages of the results obtained.     

基于响应面法的门式刚架结构可靠度分析

对钢架厂房建立了分析可靠度的计算方法.首先,使用Monte-Carlo法得到服从一定分布的随机参数,运用复合失效准则建立不同的功能函数,从而得出相应的功能函数的样本点.然后,采用二次多项式拟合相应的响应面.与常规求解结构可靠度的方法相比,本方法具有计算速度比较快的优点.     

Stochastic leader-following consensus of discrete-time nonlinear multi-agent systems with multiplicative noises

This paper studies the stochastic leader-following consensus problem of discrete-time nonlinear multi-agent systems (MASs) with multiplicative noises. The measurement information obtained from agents’ neighbors is inevitably affected by communication uncertainties, where the multiplicative noise is one of the important communication uncertainties. Multiplicative noises together with the intrinsic nonlinear dynamics bring more difficulties in the consensus control design under the leader-following topology. To solve the problem, the parameter-dependent Lyapunov functions are constructed to analyze the consensus control of first-order and second-order MASs, respectively. Some sufficient conditions, explicitly related to control gains, intensity of multiplicative noises and the Lipschitz constant regarding nonlinear functions, are established for reaching the mean square (m.s.) and almost sure (a.s.) leader-following consensus. Specifically, the obtained conditions are some scalar inequalities, which are more convenient in engineering application. Numerical simulations are conducted to validate the theoretical results.     

Powers of SPR functions and preservation properties

Basic properties of a new class of strictly positive real (SPR) functions are stated. Four problems are studied. The first deals with SPR preservation of transfer functions, obtained under the composition of polynomials with SPR0 functions. The second deals with Hurwitz stability preservation of the numerator of transfer functions, obtained under the composition of polynomials with SPR0 functions. The third deals with making a Hurwitz closed-loop plant, an SPR0 function by substituting s by SPR0 functions. The four deals with the synthesis of simultaneous SPR feedback plants. For the new class of SPR0 functions, a characterization is presented. For the first and second problems, sufficient conditions are presented using the new class of SPR0 functions. For the third and four problems, two examples are presented, the first being for simultaneous SPR closed-loop systems via constant controllers. The second is for simultaneous stabilization via universal feedback adaptive control.     

利用遥感和GIS技术监测绍兴县土地利用现状及其制图研究

以遥感影像为原始数据，应用GIS提供的空间分析功能，通过两者的结合，对土地利用的空间分布进行了定量的描述和分析，实现了快速、动态地了解和掌握土地资源的变化情况，为当地政府进行土地资源的管理提供了科学的决策依据。     

Global exponential robust stability of Cohen-Grossberg neural network with time-varying delays and reaction-diffusion terms

In this paper, the global exponential robust stability is investigated for Cohen-Grossberg neural network with time-varying delays and reaction-diffusion terms, this neural network contains time-invariant uncertain parameters whose values are unknown but bounded in given compact sets. Neither the boundedness and differentiability on the activation functions nor the differentiability on the time-varying delays are assumed. By using general Halanay inequality and M-matrix theory, several new sufficient conditions are obtained to ensure the existence, uniqueness, and global exponential robust stability of equilibrium point for Cohen-Grossberg neural network with time-varying delays and reaction-diffusion terms. Several previous results are improved and generalized, and three examples are given to show the effectiveness of the obtained results.     

Microprocessor-based simulation of sampled data systems with/without a hold device using a set of sample-and-hold functions and Dirac delta functions

In the present work, Dirac delta function (DF) set and sample-and-hold functions (SHF) set are used for microprocessor-based simulation of discrete time as well as sample-and-hold systems. Such simulations are useful for identification of control systems with known input and output sequence. The presented method utilizes operational matrices of different orders in the DF and SHF domain to develop different operational transfer functions. A few open-loop as well as closed-loop systems have been studied and the simulation results obtained are compared with exact solutions derived with the help of z-transform analysis. Experiments have also been carried out to establish the validity of the proposal.     

基于液晶光阀的可编程光学二值逻辑系统

基于液晶光阀的可编程光学二值逻辑系统张子北，刘立人（中国科学院上海光学精密机械研究所）秦伟芳（中国科学院上海技术物理研究所）摘要基于双轨编码和分束合束，本文提出一种能够实现两个二值输入变量的逻辑系统。通过控制偏振片的偏振方向，该系统能够实现所有十六种...     

Adaptive neural control of stochastic nonlinear systems with unmodeled dynamics and time-varying state delays

In this paper, a novel adaptive control scheme is investigated based on the backstepping design for a class of stochastic nonlinear systems with unmodeled dynamics and time-varying state delays. The radial basis function neural networks are used to approximate the unknown nonlinear functions obtained by using Ito differential formula and Young?s inequality. The unknown time-varying delays and the unmodeled dynamics are dealt with by constructing appropriate Lyapunov–Krasovskii functions and introducing available dynamic signal. It is proved that all signals in the closed-loop system are bounded in probability and the error signals are semi-globally uniformly ultimately bounded (SGUUB) in mean square or the sense of four-moment. Simulation results illustrate the effectiveness of the proposed design.     

An inverse quasi-static steady-state thermal stresses in a thick circular plate

The present paper deals with the determination of unknown temperature and thermal stresses on the upper surface of a thick circular plate. A thick circular plate is subjected to arbitrary known interior temperature under steady state. The fixed circular edge and lower surface of the circular plate are thermally insulated. The governing heat conduction equation has been solved by using Hankel transform methods. The results are obtained in series form in terms of Bessel's functions. The results for displacement and stresses have been computed numerically and illustrated graphically.     

Stability analysis of stochastic switching singular systems with jumps

This paper deals with the stability problem of a class of stochastic switching singular systems with jumps, where all the continuous subsystems can be unstable. By introducing multiple time-varying discretized Lyapunov functions and designing novel switching signals via mode-dependent dwell times, sufficient conditions ensuring mean square and almost sure stabilities of the considered systems are obtained. On the basis of these findings, some existing results in the literature are further generalized. We finally provide a numerical example to verify the applicability of the proposed theoretical results.     

Exponential synchronization of stochastic complex networks with multi-weights: A graph-theoretic approach

This paper concerns the exponential synchronization problem of stochastic complex networks with multiple weights (SCNMW). By the method of network split, SCNMW can be modelled as stochastic coupled systems driven by Brownian motion. By combining graph theory, Lyapunov stability theory and state feedback control technique, drive-response synchronization criteria of SCNMW have been obtained. Two kinds of exponential synchronization criteria are obtained, one is given with Lyapunov functions of vertex systems, and the other is shown with the coefficients of SCNMW. The obtained synchronization principles are closely related to the coupling strength of multiple sub-networks and the intensity of noise perturbation. Finally, a numerical example with some simulations is presented to illustrate the theoretical results.     

Global exponential robust stability of static interval neural networks with S-type distributed delays

The authors in [7] obtained the global asymptotical stability for static interval neural networks with S-type distributed delays by using the Razumikhin theorem. The aim of our paper is to investigate the global exponential robust stability by using the Lyapunov functional methods, and we will improve the proof methods more concise. A theorem and a corollary were obtained in which the boundedness, monotonicity and differentiability conditions on the activation functions are not required. So we generalize the results of related literature [7]. As an application, an example to demonstrate our results is given.     

Practical stability of discrete-time systems

Theorems are stated and proved that provide necessary and sufficient conditions for practical stability of discrete-time systems.The first part of the paper deals with stability and instability with respect to time-varying sets, whereas the second part is devoted to the study of final and semi-final stability. The conditions obtained, which take the form of existence of discrete Lyapunov-like functions, generalize previous results.     

Mean-square integral input-to-state stability of nonlinear impulsive semi-Markov jump delay systems

In this paper, the problem of mean-square integral input-to-state stability of nonlinear impulsive semi-Markov jump delay systems is investigated. By using stochastic Lyapunov functions together with Razumikhin technique, some sufficient conditions for mean-square integral input-to-state stability for a class of nonlinear impulsive semi-Markov jump delay systems are developed. In particular, the results obtained generalize and complement some recent literature. Finally, some numerical examples are given to show the effectiveness and advantages of the proposed techniques.     

Solution of integral equations using a set of block pulse functions

A set of the block pulse functions is applied to solve the Fredholm's and the Volterra's integral equations of the second kind. An algebraic equation in matrix form which is equivalent to the solution of the integral equation is developed. The approximate results are easily obtained by a few computations. An accurate solution canbe evaluated in a digital computer by solving the algebraic equation. Two examples are given.     

Model-based event-triggered multi-vehicle coordinated tracking control using reduced order models

The coordinated tracking problem where a group of followers intercepts a dynamic leader is studied. It is shown in this paper that reduction of inter-agent communication is obtained and improved performance is achieved when each follower implements dynamical models of neighbors and by using an event-triggered control strategy that requires each agent to send measurement updates only when necessary. The results in this paper consider directed graphs and the possible existence of cycles. Performance bounds on the tracking error have been obtained, which are functions of the communication topology and the event thresholds. This approach is extended to consider measurement noise and similar bounds are presented for this case.     

Some Theorems on sum Separability of Multivariable Reactance and Positive Real Functions

New necessary and sufficient conditions, which are also algorithmic in nature, are obtained for the decomposition of a multivariable reactance function or a multivariable positive real function into a sum of several single variable reactance functions or several single variable positive real functions, respectively.     

Special functions of circuits and systems

The polynomial solutions of the equation fy″ + gy′ + λy = 0 are obtained and classified for f, g, and λ certain second-degree, first-degree, and zero-degree polynomials, respectively. Applications are given illustrating the use of these polynomials in the construction of amplitude functions and system functions and in tree counting. In particular, all-pole and rational filter functions are considered which include as special cases the Chebyshev, Butterworth, elliptic, Bessel, and various transitional filter functions.     

Stochastically asymptotic stability of delayed recurrent neural networks with both Markovian jump parameters and nonlinear disturbances

In this paper we study stochastic stability of delayed recurrent neural networks with both Markovian jump parameters and nonlinear disturbances. Based on the Lyapunov stability theory, the properties of a Brownian motion, the generalized Itô's formula and linear matrix inequalities technique, some new delay-dependent conditions are derived to guarantee the stochastically asymptotic stability of the trivial solution or zero solution. In particular, the activation functions in this paper depend on Markovian jump parameters and they are more general than those usual Lipschitz conditions. Also, time delays proposed in this paper comprise both constant delays and time-varying delays. Moreover, the derivative of time delays is allowed to take any value. Therefore, the results obtained in this paper are less conservatism and generalize those given in the previous literature. Finally, two numerical examples and their simulations are used to show the effectiveness of the obtained results.