PARALLEL INTERVAL MATRIX MULTISPLITTING AOR METHODS AND THEIR CONVERGENCE

This paper proposes a class of parallel interval matrix multisplitting AOR methods far solving systems of interval linear equations and discusses their convergence properties under the conditions that the coefficient matrices are interval H-matrices.

The p-moment exponential robust stability for stochastic systems with distributed delays and interval parameters

The p-moment exponential robust stability for stochastic systems with distributed delays and interval parameters is studied. By constructing the Lyapunov- Krasovskii functional and employing the decomposition technique of interval matrix and Ito＇s formula, the delay-dependent criteria for the p-moment exponential robust stability are obtained. Numerical examples show the validity and practicality of the presented criteria.

Global stability of interval recurrent neural networks

The robust global exponential stability of a class of interval recurrent neural networks（RNNs） is studied,and a new robust stability criterion is obtained in the form of linear matrix inequality.The problem of robust stability of interval RNNs is transformed into a problem of solving a class of linear matrix inequalities.Thus,the robust stability of interval RNNs can be analyzed by directly using the linear matrix inequalities（LMI） toolbox of MATLAB.Numerical example is given to show the effectiveness of the obtained results.

Estimation of Decision Alternatives on the Basis of Interval Pairwise Comparison Matrices

This paper deals with the calculation of a vector of reliable weights of decision alternatives on the basis of interval pairwise comparison judgments of experts. These weights are used to construct the ranking of decision alternatives and to solve selection problems, problems of ratings construction, resources allocation problems, scenarios evaluation problems, and other decision making problems. A comparative analysis of several popular models, which calculate interval weights on the basis of interval pairwise comparison matrices (IPCMs), was performed. The features of these models when they are applied to IPCMs with different inconsistency levels were identified. An algorithm is proposed which contains the stages for analyzing and increasing the IPCM inconsistency, calculating normalized interval weights, and calculating the ranking of decision alternatives on the basis of the resulting interval weights. It was found that the property of weak order preservation usually allowed identifying order-related intransitive expert pairwise comparison judgments. The correction of these elements leads to the removal of contradictions in resulting weights and increases the accuracy and reliability of results.

Improved delay-dependent robust H_∞ control of an uncertain stochastic system with interval time-varying and distributed delays

In this paper, the robust H∞control problem for a class of stochastic systems with interval time-varying and distributed delays is discussed. The system under study involves parameter uncertainty, stochastic disturbance, interval time-varying,and distributed delay. The aim is to design a delay-dependent robust H∞control which ensures the robust asymptotic stability of the given system and to express it in the form of linear matrix inequalities（LMIs）. Numerical examples are given to demonstrate the effectiveness of the proposed method. The results are also compared with the existing results to show its conservativeness.

ROBUST GLOBAL EXPONENTIAL STABILITY OF UNCERTAIN IMPULSIVE SYSTEMS

By using the quasi-Lyapunov function, some sufficient conditions of global exponential stability for impulsive systems are established, which is the basis for the following discussion. Then, by employing Riccati inequality and Hamilton-Jacobi inequality approach, some sufficient conditions of robust exponential stability for uncertain linear/nonlinear impulsive systems are derived, respectively. Finally, some examples are given to illustrate the applications of the theory.

Robust Control of Permanent Magnet Synchronous Motors

In this paper, permanent magnet synchronous motors(PMSMs) are investigated. According to the feature of PMSMs, a novel state equation of PMSMs is obtained by choosing suitable state variables. Based on the state equation, robust controllers are designed via interval matrix and PI control idea.In terms of bilinear matrix inequations, sufficient conditions for the existence of the robust controller are derived. In order to reduce the conservation and the dependence on parameter,the control inputs of PMSMs are divided into two parts, a feedforward control input and a feedback control input, and relevant sufficient conditions for the existence of the controller are obtained. Because of the suitable choice of state variables, the proposed control strategies can cope with the load uncertainty and have robustness for disturbance. Finally, simulations are carried out via Matlab/Simulink soft to verify the effectiveness of the proposed control strategies. The performance of the proposed control strategies are demonstrated by the simulation results.

Research on Consistency of the Complex Interval Judgement Matrix in AHP

The weighted geometric mean method(WGMM) has been the most commonly used method in the analytic hierarchy process(AHP) for combining individual opinions to form a group opinion. In this paper, we study the consistency of the WGMM in group decision and prove that the weighted geometric mean complex interval judgement matrix (WGMIM) is of acceptable consistency under the condition that all interval matrices for the same decision\|making problem are of acceptable consistency. Thus, research on consistency of group decision in AHP is further developed and a theory basis for the application of the WGMM is also made.

面向间隔告警的多步网络攻击定量关联方法

为准确判断复杂多步攻击的意图和下一步攻击行为,需要对入侵告警进行定量关联分析。针对复杂多步攻击产生的告警在序列中经常间隔出现的实际,提出一种间隔告警定量关联方法。利用一阶马尔可夫性质建立告警关联模型,定量地表示攻击者选择不同攻击路径的可能性,利用Apriori频繁序列挖掘算法得出频繁告警2-序列的支持度,将归一化的序列支持度作为马尔可夫链的一步转移概率。利用DARPA2000真实网络数据集进行实验,实验结果表明,该方法对复杂多步攻击告警的关联准确率优于传统方法。

A Method of Synthetical Appraisal With Interval Numbers

In this paper,A method of synthetical appraisal with interval numbers is given, which combines qualitative analysis with quantitative analysis,and take quantitative analysis as the dominant factor.It is flexible and conveniente in use,It can be used in synthetical sequence for appraisal objects.

On Improved Delay-dependent Robust Stability Criteria for Uncertain Systems with Interval Time-varying Delay

This paper considers the problem of delay-dependent robust stability for uncertain systems with interval time-varying delays. By using the direct Lyapunov method, a new Lyapunov-Krasovskii(L-K) functional is introduced based on decomposition approach, when dealing with the time derivative of L-K functional, a new tight integral inequality is adopted for bounding the cross terms. Then, a new less conservative delay-dependent stability criterion is formulated in terms of linear matrix inequalities(LMIs),which can be easily solved by optimization algorithms. Numerical examples are given to show the effectiveness and the benefits of the proposed method.

Delay-dependent Non-fragile H_∞ Control for Linear Systems with Interval Time-varying Delay

This paper considers the problem of delay-dependent non-fragile H∞control for a class of linear systems with interval time-varying delay. Based on the direct Lyapunov method, an appropriate Lyapunov-Krasovskii functional(LKF) with triple-integral terms and augment terms is introduced. Then, by using the integral inequalities and convex combination technique, an improved H∞performance analysis criterion and non-fragile H∞controller are formulated in terms of linear matrix inequalities(LMIs), which can be easily solved by using standard numerical packages. At last, two numerical examples are provided to demonstrate the effectiveness of the obtained results.

ROBUST ABSOLUTE STABILITY OF GENERAL LURIE SYSTEMS WITH MULTIPLE NONLINEARITIES

The robust absolute stability of general Lurie interval direct control system with multiple nonlinearities, with respect to model variations, is considered. Some sufficient conditions of absolute stability for the system are obtained, which generalize and improve the previous results.

Parallel Solutions for Large-Scale General Sparse Nonlinear Systems of Equations

In solving application problems, many largesscale nonlinear systems of equations result in sparse Jacobian matrices. Such nonlinear systems are called sparse nonlinear systems. The irregularity of the locations of nonzero elements of a general sparse matrix makes it very difficult to generally map sparse matrix computations to multiprocessors for parallel processing in a well balanced manner. To overcome this difficulty, we define a new storage scheme for general sparse matrices in this paper. With the new storage scheme, we develop parallel algorithms to solve large-scale general sparse systems of equations by interval Newton/Generalized bisection methods which reliably find all numerical solutions within a given domain.In Section 1, we provide an introduction to the addressed problem and the interval Newton's methods. In Section 2, some currently used storage schemes for sparse sys-terns are reviewed. In Section 3, new index schemes to store general sparse matrices are reported. In Section 4, we present a parallel algorithm to evaluate a general sparse Jarobian matrix. In Section 5, we present a parallel algorithm to solve the correspond-ing interval linear 8ystem by the all-row preconditioned scheme. Conclusions and future work are discussed in Section 6.