Generalization of integral inequalities and (c_1,c_1) stability of neutral differential equations with time-varying delays

A uniform stability analysis is developed for a type of neutral delays differential equations which depend on more general nonlinear integral inequalities. Many original investigations and results are obtained. Firstly, generations of two integral nonlinear inequalities are presented, which are very effective in dealing with the complicated integro-differential inequalities whose variable exponents are greater than zero. Compared with existed integral inequalities, those proposed here can be applied to more complicated differential equations, such as time-varying delay neutral differential equations. Secondly, the notions of (ω, Ω) uniform stable and (ω, Ω) uniform asymptotically stable, especially (c1, c1) uniform stable and (c1, c1) uniform asymptotically stable, are presented. Sufficient conditions on about (c1, c1) uniform stable and (c1, c1) uniform asymptotically stable of time-varying delay neutral differential equations are established by the proposed integral inequalities. Finally, a complex numerical example is presented to illustrate the main results effectively. The above work allows to provide further applications on the proposed stability analysis and control system design for different nonlinear systems. © 2017 Beijing Institute of Aerospace Information.

Stability analysis of a noise control system in a duct by using delay differential equation

The paper deals with the criteria for the closed- loop stability of a noise control system in a duct. To study the stability of the system, the model of delay differential equation is derived from the propagation of acoustic wave governed by a partial differential equation of hyperbolic type. Then, a simple feedback controller is designed, and its closed- loop stability is analyzed on the basis of the derived model of delay differential equation. The obtained criteria reveal the influence of the controller gain and the positions of a sensor and an actuator on the closed-loop stability. Finally, numerical simulations are presented to support the theoretical results.

Stability Analysis of Stochastic Swarm Systems

In this paper, we present a model of stochastic swarm system and prove the stability of this kind of systems. We establish the stable aggregating behavior for the group using a coordination control scheme. This individual-based control scheme is a combination of attractive and repulsive interactions among the individuals in the group, which ensures the cohesion of the group and collision avoidance among the individuals. The dynamics of each individual depends on the relative positions between the individuals and the influences of the random disturbances. Under the influences of the noises, this position-based control strategy still generates the stable aggregating behavior harmoniously for the group and the self-organized swarm pattern is formed.

The Jaffa Transform for Hessian Matrix Systems and the Laplace Equation

Hessian matrices are square matrices consisting of all possible combinations of second partial derivatives of a scalar-valued initial function. As such, Hessian matrices may be treated as elementary matrix systems of linear second-order partial differential equations. This paper discusses the Hessian and its applications in optimization, and then proceeds to introduce and derive the notion of the Jaffa Transform, a new linear operator that directly maps a Hessian square matrix space to the initial corresponding scalar field in nth dimensional Euclidean space. The Jaffa Transform is examined, including the properties of the operator, the transform of notable matrices, and the existence of an inverse Jaffa Transform, which is, by definition, the Hessian matrix operator. The Laplace equation is then noted and investigated, particularly, the relation of the Laplace equation to Poisson’s equation, and the theoretical applications and correlations of harmonic functions to Hessian matrices. The paper concludes by introducing and explicating the Jaffa Theorem, a principle that declares the existence of harmonic Jaffa Transforms, which are, essentially, Jaffa Transform solutions to the Laplace partial differential equation.

A DELAY-DEPENDENT STABILITY CRITERION FOR NONLINEAR STOCHASTIC DELAY-INTEGRO-DIFFERENTIAL EQUATIONS

A type of complex systems under both random influence and memory effects is considered. The systems are modeled by a class of nonlinear stochastic delay-integrodifferential equations. A delay-dependent stability criterion for such equations is derived under the condition that the time lags are small enough. Numerical simulations are presented to illustrate the theoretical result.

一类Caputo-Katugampola型分数阶微分方程耦合系统边值问题

利用Leray-Schauder二择一定理和Schauder不动点定理,研究了一类具有Caputo-Katugampola型导数的分数阶微分方程耦合系统边值问题解的存在唯一性,再利用Banach不动点定理和Ulam-Hyers稳定性的定义,讨论了该边值问题的Ulam-Hyers稳定性.

HIERARCHICAL ITERATION METHOD TO SOLVE DYNAMIC DIFFERENTIAL EQUATION

The dynamic differential equation of a multibody System can be presented inthe form of Aq= B. Calculating the inverse of matrix A is a simple way to solve this kindof differential equatbo. Matrix A will be in the ill condition if the system is configured asa main they with small mass appendages. A hierarchical iteration method is given in thispaper to avoid the problem of the inverse of an ill condition matrix calculatbo. It is pont-ed out that the stability of the system input and output is the suffcient condition of itera-tion convergence. The method omits a series formula expanding step. It is also useful toreduce the immuence of the stiff problem. The calculation progress i8 modular and structural.

Infinite horizon LQR for systems with multiple delays in a single input channel

This paper is concerned with the linear quadratic regulation （LQR） problem for both linear discrete-time systems and linear continuous-time systems with multiple delays in a single input channel. Our solution is given in terms of the solution to a two-dimensional Riccati difference equation for the discrete-time case and a Riccati partial differential equation for the continuous-time case. The conditions for convergence and stability are provided.

A CLASS OF KOLMOGOROV'S ECOLOGICAL SYSTEM WITH PREY HAVING CONSTANT ADDING RATE

In this paper, by using the qualitative method, we study a class of Kolmogorov 's ecological system with prey having constant adding rate, discuss the relative position and the character of the equilibriums, the global stability of the practical equilibriums and give a group of conditions for the boundedness of the solutions, the nonexistence, the existence and the uniqueness of the limit cycle of the system. Most results obtained in papers [1] and [2] are included or generalized.

Modelling the Dynamical State of the Projected Primary and Secondary Intra-Solution-Particle Movement System of Efavirenz In-Vivo

This work seeks to describe intra-solution particle movement system. It makes use of data obtained from simulations of patients on efavirenz. A system of ordinary differential equations is used to model movement state at some particular concentration. The movement states’ description is found for the primary and secondary level. The primary system is found to be predominantly an unstable system while the secondary system is stable. This is derived from the state of dynamic eigenvalues associated with the system. The saturated solution-particle is projected to be stable both for the primary potential and secondary state. A volume conserving linear system has been suggested to describe the dynamical state of movement of a solution particle.

直流配电系统主从控制下的随机稳定性分析

分布式电源的间歇性波动以及储能、电动汽车反复充放电等随机因素对直流配电系统的稳定运行带来了极大的挑战。首先,文中针对主从控制下直流配电系统的随机激励,建立了降阶随机微分方程,推导了系统随机微分方程的解析解。然后,建立了均值及均方稳定性的解析化判据,全面刻画了小扰动稳定与均值及均方稳定的关系,推导出小扰动不稳定但均值均方稳定的判据。最后,通过仿真及实验验证了理论分析的有效性。

一类非线性Caputo型分数阶微分方程耦合系统解的存在性和稳定性

研究一类非线性Caputo型分数阶微分方程耦合系统的边值问题。首先,将方程转化为等价的积分方程;其次,利用Leray-Schauder抉择和Banach压缩映像原理讨论该边值问题解的存在性和唯一性的充分条件;最后,分析该耦合系统的Ulam-Hyers、Ulam-Hyers-Rassias和Ulam-Hyers-Mittag-Leffer稳定性。

Asymptotic Stability Criteria for Singular Differential Nonlinear Systems with Time-Varying Delays

In this paper, the asymptotic stability for singular differential nonlinear systems with multiple time-varying delays is considered. The V-functional method for general singular differential delay system is investigated. The asymptotic stability criteria for singular differential nonlinear systems with multiple time-varying delays are derived based on V-functional method and some analytical techniques, which are described as matrix equations or matrix inequalities. The results obtained are computationally flexible and efficient.

高斯-泊松激励影响下新型电力系统的稳定性研究

随着可再生能源、电力电子设备接入数量的不断增加,新型电力系统在向电气化和清洁化方向发展的同时,带来了更多、更大强度外部激励的影响。为了解外部激励对新型电力系统稳定性的影响,针对高斯激励和泊松激励,文章从数值域视角出发,提出了一种电力系统稳定性分析方法。其首先分别刻画了高斯激励和泊松激励的随机特性,并建立了高斯-泊松激励下的电力系统随机动态模型;然后,基于预估校正思想,构造了Milstein-Euler数值计算方法,并对所建的模型进行迭代求解;最后,定量分析了不同激励强度对新电力系统稳定性的影响。算例分析结果验证了高斯-泊松激励下电力系统随机动态模型和Milstein-Euler数值计算方法的正确性与合理性。文中所提模型和方法可为随机因素影响下的电力系统建模仿真提供参考,为电力系统安全运行、优化控制提供支撑。

FUNCTIONAL DIFFERENTIAL INEQUALITIES AND TIME-DELAY STOCHASTIC SYSTEMS (Ⅳ)——CRITERIA FOR PRACTICAL STABILITY

Ⅰ. INTRODUCTIONIn the real world, many practical systems may be unstable in the sense of Lyapunov but are stable in the sense of practical stability introduced by LaSalle and Lefschetz. For ex-ample, an aircraft or a missile may move along an orbit which is unstable in the sense of Lyapunov, but it is practically stable. For deterministic systems, the results of a

双时间尺度电力系统动态模型降阶研究(一)——电力系统奇异摄动模型

电力系统是一个多时间尺度的大规模非线性系统 ,其稳定性分析非常复杂。为提高稳定计算的效率 ,对复杂的电力系统模型进行化简 ,以实现系统化降阶非常必要。文中以电力系统物理电路为基础 ,导出了一个计及电磁快动态的电力系统奇异摄动模型。推导中 ,以感应电动机并联线性阻抗为负荷模型 ,并考虑了线路充电电容与负荷补偿电容。该模型是一个标准的双时间尺度模型 。

动态区间系统的鲁棒稳定性

研究了动态连续区间系统和离散区间系统的鲁棒稳定性问题 .在给出了区间系统的一种等价描述之后 ,利用Lyapunov方法和Riccati方程方法 ,分别得到了连续区间系统和离散区间系统鲁棒稳定的充分条件 .最后的数值例子说明本文的结果不仅保守性小 。

电力系统在线暂态稳定分析方法

提出了一种电力系统在线暂态稳定分析方法。结合故障时域仿真,建立了一个2维1阶微分方程组。该微分方程组描述了相点在一维坐标轴上的运动,可用于观察电力系统的功角稳定性。在此基础上提出的功角稳定判据可以方便地判断电力系统的功角稳定性。该方法有效地简化了暂态稳定分析过程,且避免了因功角差阈值选取不当造成误判的问题。文中还研究了针对相点运动构造的能量函数,利用故障后的最小动能定义了描述故障严重程度的稳定指标。2007年华北电网的算例说明了上述方法的有效性。

基于延拓法的电力系统稳定模型中二维参数局部分岔边界的计算

该文提出表示微分-代数模型中的奇异性、鞍结点和霍普夫分岔的代数方程以便应用延拓法来求解获得二维参数的分岔边界。该方程保留了电力系统稳定微分-代数模型的形式不变,也未涉及到矩阵求逆或行列式值的计算,同时该方程也具有直接法计算分岔时速度快的优点。其缺点是方程的维数增加了。应用所提方法计算了一简单电压稳定和一多机电力系统稳定模型中的二维参数局部分岔边界,并和实域仿真进行比较,结果表明该方法是准确可行的。

区间系统的鲁棒稳定性

对于鲁棒稳定的区间系统 ,基于对系统自身结构特征的分析和信息的提取 ,利用矩阵不等式方法构造系统的Lyapunov方程的对称正定解 ,进而得到了若干判别区间系统鲁棒稳定的充分性条件 .