共查询到20条相似文献，搜索用时 375 毫秒
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本文推导了双三角—U型槽组合阀口面积计算方法和计算公式,在MATLAB软件里建立了阀口面积的计算程序,同时采用多项式分段对该组合阀口过流面积曲线进行拟合,分别得到阀口面积A(x)、面积W(x)梯度表达式。 相似文献
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应用反射函数建立了多项式微分方程x=Pn(t,x)与其扰动方程x=Pn(t,x)+α(t)Δ(t,x)之间的等价关系,并给出了当Δ(t,x)=Qn(t,x)时,它们之间等价的充分条件.这一结论是对文献[4]中相关结论的推广. 相似文献
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定义:函数f(x)如果对其定义域中任意的x1、x2都有如下不等式成立,即f(x1+x2/2)≤f(x1)+f(x2)/2则称f(x)为下凸函数,等号当且仅当x1=x2时成立.如果总有f(x1+x2/2)≥f(x1)+f(x2)/2则称f(x)为上凸函数,等号当且仅当x1=x2时成立.…… 相似文献
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沈忠民 《中国科学院研究生院学报》1986,(1)
本文研究了高次多项式系统的极限环数目。如果记 P_n 表示次数不大于 n 的实系数多项式全体,我们定义多项式系统(dx)/(dt)=f(x,y)(dy)/(dt)=g(x,y)(1)的 Hilbert 数 H(n)如下H(n){系统(1)的极限环数目}则有定理:如果 p,q 为任意正整数,它们满足 p|q,则(H(q-1))/q~2≥(H(p-1))/p~2 相似文献
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利用多项式环F[x]上的欧几里德算法给出求解多项式环F[x]上的多元一次不定方程通解的矩阵解法，同时利用MATLAB数学软件给出相应的计算机求解多项式环F[x]上一次不定方程的程序，这种方法可以普遍地应用． 相似文献
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周赟 《中国科学院研究生院学报》2007,24(6):725-728
设K为代数闭域k的有限生成扩域.C:f(x)=ayn为K上曲线,其中f是k上至少有3个单零点的多项式且n>3是正整数,n不是域k的特征的倍数,再设a■Kn,那么曲线C不能定义在k上,即曲线C:(x)=ayn不会k(a)同构于一条k上的曲线. 相似文献
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李挨元 《内蒙古科技与经济》2002,(Z1)
形如 |x a| |x b|c (2 ) (c>0 )的不等式 ,其一般解法是按照绝对值的意义 ,用零点分段法去求解 ,但解起来比较麻烦 ,下面讨论一种简单解法。|x a|和 |x b|的几何意义是数轴上的点分别距 - a和 - b这两数的距离 ,所以 |x a| |x b|是数 x到 - a与- b两 相似文献
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1。在滤波器设计中,需要求“乘积多项式” F(x)=P(x) K一Q(x)(1)的所有实二次因子,其中P(x),Q(x)都是形为n(x一ri)或fl(x“一vi,x一v,:)的多项 i=11=1式,而K,r,,vi:,v;2均为实数(参见〔z〕)。为此,通常先将(1)转化为F(x)=艺a;xN一i(2)的形式,然后用Bairstow方法求解,当求得一个二次因子以后,以此因子除F(x),使之降次,继续对商多项式使用Bairstow方法。但计算过程中的舍入误差将严重影响计算精度。为避免降次过程的误差积累,可以如〔2〕中那样进行“精炼”,但数值实践表明,这种精炼过程也隐藏着危险性:虽然降次后求得的某二次因子已比较… 相似文献
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Recently, a polynomials-based integral inequality was proposed by extending the Moon’s inequality into a generic formulation. By imposing certain structures on the slack matrices of this integral inequality, this paper proposes an orthogonal-polynomials-based integral inequality which has lower computational burden than the polynomials-based integral inequality while maintaining the same conservatism. Further, this paper provides notes on relations among recent general integral inequalities constructed with arbitrary degree polynomials. In these notes, it is shown that the proposed integral inequality is superior to the Bessel–Legendre (B–L) inequality and the polynomials-based integral inequality in terms of the conservatism and computational burden, respectively. Moreover, the effectiveness of the proposed method is demonstrated by an illustrative example of stability analysis for systems with additive time-varying delays. 相似文献
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《Journal of The Franklin Institute》2022,359(11):5750-5777
This paper is concerned with the problem of exponentially extended dissipative criteria for a class of delayed discrete-time neural networks (DNNs) subject to resilient observer-based controller design. For this objective, a memoryless full-order Luenberger state observer is designed, and further, its observer error system is calculated with resilient control. Initially, some new improved weighted summation inequalities are proposed by combining weighted summation inequality and an extended reciprocal convex matrix inequality. By constructing the suitable Lyapunov-Krasovskii functional (LKF) and utilizing the developed summation inequalities, the exponentially extended dissipative criterion is obtained for the considered delayed DNNs. The designed observer and resilient control gain matrices can be determined by solving a set of linear matrix inequalities (LMIs) subject to the prescribed exponential decay rate. Finally, two numerical examples are carried out to illustrate the feasibility and effectiveness of the established theoretical results obtained through the newly developed summation inequalities. 相似文献
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通过建立一个权函数的不等式,改进了Hilbert定理,作为应用,建立了一个Hilbert类积分不等式及其加强式。 相似文献
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通过引入参数λ,应用改进的Muler-Maclaurin求和公式,给一个Hardy-Hilbert型不等式以具有最佳常数因子的推广,作为应用,给出了它的等价形式。 相似文献
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This paper presents a new necessary and sufficient condition for testing the strong delay-independent stability of linear systems subject to a single delay. The proposed method follows from the use of matrix polynomials constraints and the Kalman–Yakubovich–Popov lemma. The resulting condition can be checked exactly by solving a feasibility problem in terms of a linear matrix inequality (LMI). Simple numerical examples are given to show the effectiveness of the proposed method. 相似文献
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On the time-varying Halanay inequality with applications to stability analysis of time-delay systems
Haifang Li Bin Zhou Mingzhe Hou Guangren Duan 《Journal of The Franklin Institute》2021,358(10):5488-5512
The main results of the paper are improvements on the stability analysis of Halanay inequalities with time-varying coefficients in both continuous-time and discrete-time setting. Three classes of improved conditions are established to ensure that the solution to the Halanay inequality is uniformly exponentially stable. The merit of the proposed new conditions is that the coefficients of the Halanay inequality can be unbounded and sign indefinite. This is achieved by using the notion and properties of uniformly asymptotic stable (UAS) functions. Based on the improved stability conditions for the Halanay inequality and the Lyapunov Razumikhin approach, three classes of sufficient conditions are established for testing the stability of time-varying time-delay systems. Finally, the advantages of the proposed methods are illustrated by some numerical examples with some of them borrowed from the literature. 相似文献
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This paper is concerned with the stochastic synchronization problem for a class of Markovian hybrid neural networks with random coupling strengths and mode-dependent mixed time-delays in the mean square. First, a novel inequality is established which is a double integral form of the Wirtinger-based integral inequality. Next, by employing a novel augmented Lyapunov–Krasovskii functional (LKF) with several mode-dependent matrices, applying the theory of Kronecker product of matrices, Barbalat’s Lemma and the auxiliary function-based integral inequalities, several novel delay-dependent conditions are established to achieve the globally stochastic synchronization for the mode-dependent Markovian hybrid coupled neural networks. Finally, a numerical example with simulation is provided to illustrate the effectiveness of the presented criteria. 相似文献
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In this paper, a composite Chebyshev finite difference method for solving linear quadratic optimal control problems with inequality constraints on state and control variables is introduced. This method is an extension of Chebyshev finite difference scheme and is based on a hybrid of block-pulse functions and Chebyshev polynomials using the well known Chebyshev–Gauss–Lobatto nodes. The excellent properties of hybrid functions are used to convert optimal control problem into a mathematical programming problem whose solution is much more easier than the original one. Various types of optimal control problems are investigated to demonstrate the effectiveness of the proposed approximation scheme. The method is simple, easy to implement and provides very accurate results. 相似文献
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M.H. Heydari 《Journal of The Franklin Institute》2019,356(15):8216-8236
The main goal of this study is to develop an efficient matrix approach for a new class of nonlinear 2D optimal control problems (OCPs) affected by variable-order fractional dynamical systems. The offered approach is established upon the shifted Chebyshev polynomials (SCPs) and their operational matrices. Through the way, a new operational matrix (OM) of variable-order fractional derivative is derived for the mentioned polynomials.The necessary optimality conditions are reduced to algebraic systems of equations by using the SCPs expansions of the state and control variables, and applying the method of constrained extrema. More precisely, the state and control variables are expanded in components of the SCPs with undetermined coefficients. Then these expansions are substituted in the cost functional and the 2D Gauss-Legendre quadrature rule is utilized to compute the double integral and consequently achieve a nonlinear algebraic equation.After that, the generated OM is employed to extract some algebraic equations from the approximated fractional dynamical system. Finally, the procedure of the constrained extremum is used by coupling the algebraic constraints yielded from the dynamical system and the initial and boundary conditions with the algebraic equation extracted from the cost functional by a set of unknown Lagrange multipliers. The method is established for three various types of boundary conditions.The precision of the proposed approach is examined through various types of test examples.Numerical simulations confirm the suggested approach is very accurate to provide satisfactory results. 相似文献
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《Journal of The Franklin Institute》2022,359(9):4019-4053
In this paper, several resultful control schemes based on data quantization are proposed for complex-valued memristive neural networks (CVMNNs). Firstly, considering the finite communication resources and the interference of failures to the system, a state quantized sampled-data controller (SQSDC) is designed for CVMNNs. Next, taking the interference of gain fluctuations into account, a non-fragile sampled-data control (SDC) law is proposed for CVMNNs in the framework of data quantification. In order to full capture more inner sampling information, a newly Lyapunov-Krasovskii function (LKF) is constructed on the basis of the proposed triple integral inequality. After that, in the framework of taking full advantage of the property of Bessel-Legendre inequality, a time-dependent discontinuous LKF (TDDLKF) is proposed for CVMNNs with SQSDC. Based on the useful LKF, several stability criteria are established. Finally, the numerical simulations are provided to substantiate the validity and less conservatism of the proposed schemes. 相似文献