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1.
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.  相似文献   

2.
首先在一元模糊反映射存在一对多的情况下,给出隶属度函数的一种求取算法,用以改善模糊映射为一元函数时的模糊性传递;其次,在一定假设条件下,提出一般多元函数的模糊性传递原理,并给出证明;最后,借鉴边际概率分布的计算公式,针对多元隶属度函数已知的情形,给出求取单个变量的隶属度函数公式,并进行了相应证明.  相似文献   

3.
章劲鸥 《科技通报》2008,24(3):299-304
通过态射的分解讨论预加法范畴中态射的Moore-Penrose逆。给出了态射的Moore-Penrose逆存在的几个充要条件以及表达式。特别,得到了态射f有Moore-Penrose逆的充要条件是f有泛分解f=pgq使得g 存在并且(pg)*pg i-g g和gq(gq)* i-gg 均可逆。  相似文献   

4.
This paper discusses a multivariable array whose elements are multivariable homogeneous polynomials which may have missing terms in any of the variables. This array permits one to obtain conditions for the realizability of a driving-point function or a transfer function as a resistively terminated low-pass ladder network. By reac- tance transformations, other forms of ladder structures can be obtained. The case of cascade-separable ladder networks is discussed in detail.  相似文献   

5.
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   

6.
A sequence of metrics {DN} is said to be additive and matched to a discrete memoryless channel (DMC) if DN is the sum on its coordinates of N single letter metrics and if the maximum likelihood decoder for sequences of length N is a minimum DN-distance decoder. Necessary and sufficient conditions on the transition probabilities of a DMC for the existence of a sequence of additive metrics matched to it are given. In the case of the binary channel these are shown to be equivalent to the channel being symmetric. Explicit transition probabilities are given for a large class of ternary DMCs with an associated sequence of additive matched metrics. The problem solved here may be considered a generalization of the problem of finding the DMCs matched to the Lee metric solved by Chiang and Wolf in 1971 (2).  相似文献   

7.
This paper mainly presents Routh-type table test methods for zero distribution of polynomials with commensurate fractional degrees on the left-half plane, right-half plane and imaginary axis in the complex plane. The proposed tabular methods are derived for extension and generalization of the Routh test, which is widely used in controls for zero distribution of polynomials with integer degrees. Singular cases are discussed and handled efficiently and simply. Necessary and sufficient conditions for the second singular case are completely analyzed in terms of symmetric zeros. A particular property is revealed that a polynomial with commensurate fractional degrees without pure imaginary zero may still be stable in the presence of the second singular case, which is impossible for a real polynomial with integer degrees. Furthermore, we present a test to solve the zero distribution problem with respect to general sector region for polynomials with commensurate fractional degrees and real/complex coefficients. Finally, numerical examples are given to illustrate the correctness and effectiveness of the results. The proposed methods have broad application areas, including various systems, circuits and control.  相似文献   

8.
We investigate the input–output decoupling problem of switched Boolean control networks (SBCNs) in this paper. Based on the matrix expression of Boolean functions, the dynamics of SBCNs are converted into an algebraic form via semi-tensor product of matrices first. Then, using the redundant variable separation technique, we give the necessary and sufficient conditions for the existence of three kinds of controllers to detect whether an SBCN can be input–output decomposed or not, respectively, including the open-loop controllers, the state feedback controllers, and the output feedback controllers. Meanwhile, a constructive procedure is presented to construct the open-loop controllers, as well as the state feedback controllers and output feedback controllers. Finally, an illustrative example is given to show that the new results obtained are effective.  相似文献   

9.
A study is made of the orthogonal polynomials on certain curves in the complex plane. Necessary and sufficient conditions for a set of polynomials to be orthogonal on the curves are obtained in terms of symmetric matrices. The relations of the symmetric matrices to Toeplitz matrices and innerwise matrices are shown.  相似文献   

10.
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.  相似文献   

11.
A numerical method for solving the higher order linear difference equations with variable coefficients and mixed argument under the mixed conditions is presented. The method is based on the hybrid Legendre and Taylor polynomials. The solution is obtained in terms of Legendre polynomials. IIIustrative examples are included to demonstrate the validity and applicability of the technique.  相似文献   

12.
When an operation is carried out on polynomials or power series the result is usually a new power series. The general term of the series is the product of a multiplier which depends on the operation being performed and another factor which is common to the power series being operated on. In this paper equations are developed for the general term of the resultant series when certain operations are carried out on a series or on several series. Convenient equations are given for obtaining those factors common to a given series, and the lower order factors are tabulated. Several useful examples are given.  相似文献   

13.
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.  相似文献   

14.
This paper proposes a time domain approach to deal with the regional eigenvalue-clustering robustness analysis problem of linear uncertain multivariable output feedback proportional-integral-derivative (PID) control systems. The robust regional eigenvalue-clustering analysis problem of linear uncertain multivariable output feedback PID control systems is converted to the regional eigenvalue-clustering robustness analysis problem of linear uncertain singular systems with static output feedback controller. Based on some essential properties of matrix measures, a new sufficient condition is proposed for ensuring that the closed-loop singular system with both structured and mixed quadratically-coupled parameter uncertainties is regular and impulse-free, and has all its finite eigenvalues retained inside the same specified region as the nominal closed-loop singular system does. Two numerical examples are given to illustrate the application of the presented sufficient condition.  相似文献   

15.
考虑如下用来描述浮游动物-营养物相互作用时滞微分方程模型 其中 是营养物浓度, 是浮游动物种群的度量,并且参数 为正常数. 如果 成立, 则该系统的正平衡点是全局吸引的. 也给出了正平衡点局部稳定的充分条件. （编辑：摘要中有公式,但未能正常显示）  相似文献   

16.
In this paper, we present necessary and sufficient stability and robust stability conditions for two-dimensional (2D) systems described by the Fornasini-Marchesini (FM) second model in terms of the discriminant systems of polynomial. This paper simplifies the traditional method of stability into a tractable method by the fractional linear transformation (FLT). More specifically, we reduce the stability analysis to a easy issue whether some polynomials are positive definite. Then we use the same idea to consider the stabilization and robust stabilization issues. Finally, the effectiveness of the proposed results is demonstrated by a practical example and two numerical examples.  相似文献   

17.
In this paper, the discrete-time fuzzy cellular neural network with variable delays and impulses is considered. Based on M-matrix theory and analytic methods, several simple sufficient conditions checking the global exponential stability and the existence of periodic solutions are obtained for the neural networks. Moreover, the estimation for exponential convergence rate index is proposed. The obtained results show that the stability and periodic solutions still remain under certain impulsive perturbations for the neural network with stable equilibrium point and periodic solutions. Some examples with simulations are given to show the effectiveness of the obtained results.  相似文献   

18.
The operational properties of the integration and product of Chebyshev polynomials are used in the analysis of bilinear systems by the approximation of time functions by truncated Chebyshev series. The operational properties are also applied to determine the unknown parameters of a general bilinear system from the input-output data. Examples with excellent results are given.  相似文献   

19.
This paper is concerned with the linear quadratic (LQ) Pareto game of the stochastic singular systems in infinite horizon. Firstly, the optimal control problem of the weighted sum cost functional is discussed. Utilizing the equivalent transformation method, the weighted sum LQ optimal control problem is transformed into a stochastic LQ optimization problem. Based on the classical stochastic LQ optimal control theory, the necessary and sufficient condition for the solvability of the indefinite weighted sum LQ optimal control is put forward. Then, the LQ Pareto game of the stochastic singular systems is studied. By the discussion of the convexity of the cost functionals, a sufficient condition for the existence of the Pareto solutions is obtained via the solvability of the corresponding generalized algebraic Riccati equation (GARE). Moreover, we derive all Pareto solutions based on the solution of a Lyapunov equation. Finally, an example is given to show the effectiveness of the proposed results.  相似文献   

20.
This study considers the stability problem of a flexible-joint robot in case time delays are involved in the feedback loop. We assume in our analysis that the controller uses only position measurements. The single and multiple time-delay cases, are considered. By using some useful structural properties of the robot model, sufficient conditions for asymptotic (exponential) stability of the system under consideration have been established. An estimate to the system rate of convergence is given and a procedure for evaluating the region of attraction, is given.  相似文献   

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