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1.
The construction of nomographs for transitional classical filters is described. Gain functions of classical filters are related to filter requirements resulting in a formulation for the general gain nomograph. The transitional filters that are products of approximating polynomials are incorporated into the general gain nomograph resulting in transitional filter nomographs that are sums of the individual nomographs. Nomographs for transitional filters using alternative forms where poles are interpolated are also considered. The resulting nomographs allow for quick optimization of transitional filter frequency response in many cases. Design examples are submitted and discussed. The proposed transitional filter nomographs provide the engineer with increased insight into the selection of classical transitional filters with optimum frequency response.  相似文献   

2.
This paper analyses the linear time-varying system by the shifted Legendre polynomials expansion. Using the operational matrix for integrating the shifted Legendre polynomials, the dynamic equation of a linear time-varying system is reduced to a set of simultaneous linear algebraic equations. The coefficients of the shifted Legendre polynomials expansion can be determined by using the least-squares method. An example is given to demonstrate the accuracy of shifted Legendre polynomials expansion of finite terms and it is compared with the results of the Laguerre method.  相似文献   

3.
In this paper, we use Legendre wavelet method for solving quadratic Riccati differential equations and perform a comparative study between the proposed method and other existing methods. Our results show that in comparison with other existing methods, the Legendre wavelet method provides a fast convergent series of easily computable components. The present study is illustrated by exploring two kinds of nonlinear Riccati differential equations that shows the pertinent features of the Legendre wavelet method.  相似文献   

4.
Nomographs for determining the filter order of classical filters based on selectivity requirements are presented. The selectivities for a variety of standard classical filters are summarized in equation form and the general selectivity nomograph is constructed. The selectivity equations are then converted into nomograph form by applying the relationship between the transfer function and the response slope. Design examples are presented to demonstrate the usefulness of the selectivity nomographs. These nomographs can be used to gauge filter performance and combined with optimization techniques can yield superior classical filter designs.  相似文献   

5.
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   

6.
In the present paper, a new Legendre wavelet operational matrix of derivative is presented. Shifted Legendre polynomials and their properties are employed for deriving a general procedure for forming this matrix. The application of the proposed operational matrix for solving initial and boundary value problems is explained. Then the scheme is tested for linear and nonlinear singular examples. The obtained results demonstrate efficiency and capability of the proposed method.  相似文献   

7.
谷峰 《科技通报》2008,24(3):310-314
提出了仅用基本运算加,减,移位计算勒让德多项式的坐标旋转算法,证明了算法的收敛性,讨论了算法的误差估计。  相似文献   

8.
A method of using orthogonal shifted Legendre polynomials for identifying the parameters of a process whose behaviour can be modelled by a linear differential equation with time-varying coefficients in the form of finite-order polynomials is presented. It is based on the repeated integration of the differential equation and the representations of ∫0ts(τ) dτ = Ps(t) and ts(t) = Rs(t), where P and R are constant matrices and s(t) is a shifted Legendre vector whose elements are shifted Legendre polynomials. The differential input-output equation is converted into a set of overdetermined linear algebraic equations for a least squares solution. The results of simulation studies are included to illustrate the applicability of the method.  相似文献   

9.
By applying hybrid functions of general block-pulse functions and Legendre polynomials, the linear-quadratic problem of linear time-varying systems with delays are transformed into the optimization problem of multivariate functions. The approximate solutions of the optimal control and state as well as the optimal value of the objective functional are derived. The numerical examples illustrate that the algorithms are valid.  相似文献   

10.
By applying hybrid functions of general block-pulse functions and Legendre polynomials, linear Volterra integrodifferential systems are converted into a system of algebraic equations. The approximate solutions of linear Volterra integrodifferential systems are derived. Using the results we obtain the optimal control and state as well as the optimal value of the objective functional. The numerical examples illustrate that the algorithms are valid.  相似文献   

11.
A method for finding the optimal control of a linear time varying delay system with quadratic performance index is discussed. The properties of the hybrid functions which consists of block-pulse functions plus Legendre polynomials are presented. The operational matrices of integration, delay and product are utilized to reduce the solution of optimal control to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.  相似文献   

12.
A finite series expansion method using discrete Legendre orthogonal polynomials (DLOPs) is applied to analyze linear time-varying discrete systems. An effective algorithm is derived to establish a representation which relates the DLOP coefficient vector of a product function to those of its two-component functions. By using this representation, along with the time-shift operational matrix of DLOP, a linear time-varying difference equation is converted into a set of linear algebraic equations. It is therefore convenient for computer computation.  相似文献   

13.
In this work, we have investigated the problem of assessing stability and designing an appropriate feedback control law for T-S fuzzy systems with time-varying delay. By way of designing a new Lyapunov-Krasovskii functional based on Legendre polynomials and membership functions, we have developed conditions for stability assessment and feedback gain synthesis. The resulting algebraic conditions form a set of hierarchical LMIs which, by increasing the order of the Bessel-Legendre polynomial, compete with the sum of squares in both conservatism and complexity. Finally, two examples are provided to demonstrate the effectiveness of the findings.  相似文献   

14.
The linear Legendre mother wavelets operational matrix of integration P is derived. A general procedure of forming this matrix P is given. This matrix P can be used to solve problems such as calculus of variations, differential equations, optimal control and integral equations. Illustrative examples are included to demonstrate the validity and applicability of matrix P.  相似文献   

15.
An adaptive numerical method for solving multi-delay optimal control problems with piecewise constant delay functions is introduced. The proposed method is based on composite pseudospectral method using the well-known Legendre–Gauss–Lobatto points. In this approach, the main problem converts to a mathematical optimization problem whose solution is much more easier than the original one. The necessary conditions of optimality associated to nonlinear piecewise constant delay systems are derived. The method is easy to implement and provides very accurate results.  相似文献   

16.
This paper proposes Discrete Legendre Polynomial(DLP)-based inequality by solving the best weighted approximation of a given time series. The proposed inequality could significantly reduce the conservativeness in stability analysis of systems with constant or interval time-varying delays. Also former well-known integral inequities, such as discrete Jensen inequality, discrete Wirtinger-based inequality, are both included in the proposed DLP-based inequality as special cases with lower-order approximation. Stability criterion with less conservatism is then developed for both constant and time-varying delayed systems. Several numerical examples are given to demonstrate the effectiveness and benefit of the proposed method.  相似文献   

17.
Using block-pulse functions (BPFs)/shifted Legendre polynomials (SLPs) a unified approach for computing optimal control law of linear time-varying time-delay systems with reverse time terms and quadratic performance index is discussed in this paper. The governing delay-differential equations of dynamical systems are converted into linear algebraic equations by using operational matrices of orthogonal functions (BPFs and SLPs). The problem of finding optimal control law is thus reduced to the problem of solving algebraic equations. One example is included to demonstrate the applicability of the proposed approach.  相似文献   

18.
This paper addresses the delay-dependent stability problem of linear systems with interval time-varying delays. A generalized free-matrix-based inequality is proposed and employed to derive stability conditions, which are less conservative than the Bessel–Legendre inequality. An augmented Lyapunov–Krasovskii functional is tailored for the generalized free-matrix-based inequality. Then, some items in the Lyapunov–Krasovskii functionals are integrated so as to relax its positive definite condition, which provides a more accurate lower bound for the Lyapunov–Krasovskii functionals. Therefore, some less conservative stability criteria are presented. Two numerical examples illustrate the effectiveness of the method.  相似文献   

19.
This paper is concerned with the admissibility analysis for the singular system with a periodically time-varying delay. By dividing the periodic delay interval into monotonically decreasing and increasing intervals, a novel Lyapunov–Krasovskii functional (LKF) is developed in virtue of the looped functional philosophy, relaxing the positive definition of the LKF and making full use of the system state and the time-varying delay function information. Then, a new admissibility condition is derived by combining the newly constructed LKF and the second-order canonical Bessel–Legendre integral inequality. Finally, two numerical examples are given to demonstrate the superiority of the developed method.  相似文献   

20.
A systematic treatment of the thermodynamic properties of electromagnetic fields is presented. Many potential difficulties are avoided by using the pre-existing electric and magnetic fields as thermodynamic variables. Four sets of thermodynamic functions of state may be defined, all of which are interrelated by Legendre transformations, and 96 Maxwell relations may be derived. The functions of state expressed in terms of the pre-existing electromagnetic field variables are then used to determine how the various thermodynamic quantities of interest vary with the applied fields. The analysis points to the need for carefully redefining the pressure when dealing with magnetic fields rather than magnetization as the fundamental independent variable.  相似文献   

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