共查询到20条相似文献,搜索用时 31 毫秒
1.
2.
We consider the problem of finding interval enclosures of all zeros of a nonlinear system of polynomial equations. We present a method which combines the method of Gröbner bases (used as a preprocessing step), some techniques from interval analysis, and a special version of the algorithm of E. Hansen for solving nonlinear equations in one variable. The latter is applied to a triangular form of the system of equations, which is generated by the preprocessing step. Our method is able to check if the given system has a finite number of zeros and to compute verfied enclosures for all these zeros. Several test results demonstrate that our method is much faster than the application of Hansen’s multidimensional algorithm (or similar methods) to the original nonlinear systems of polynomial equations. 相似文献
3.
We present a symbolic algorithm to solve for the zeros of a polynomial vector field equivariant with respect to a finite subgroup of O (n). We prove that the module of equivariant. polynomial maps for a finite matrix group is Cohen-Macaulay and give an algorithm to compute a fundamental basis. Equivariant normal forms are easily computed from this basis. We use this basis to transform the problem of finding the zeros of an equivariant map to the problem of finding zeros of a set of invariant polynomials. Solving for the values of fundamental polynomial invariants at the zeros effectively reduces each group orbit of solutions to a single point. Our emphasis is on a computationally effective algorithm and we present our techniques applied to two examples. 相似文献
4.
A new definition of transmission zeros for a linear, multivariable, time-invariant system is made which is shown to be equivalent to previous definitions. Based on this new definition of transmission zeros, new properties of transmission zeros of a system are then obtained; in particular, it is shown that a system with an unequal number of inputs and outputs almost always has no transmission zeros and that a system with an equal number of inputs and outputs almost always has either n−1 or n transmission zeros, where n is the order of the system; transmission zeros of cascade systems are then studied, and it is shown how the transmission zeros of a system relate to the poles of a closed loop system subject to high gain output feedback. An application of transmission zeros to the servomechanism problem is also included. A fast, efficient, numerically stable algorithm is then obtained which enables the transmission zeros of high order multivariable systems to be readily obtained. Some numerical examples for a 9th order system are given to illustrate the algorithm. 相似文献
5.
In order to perform the rigorous computation of the zeros of Bessel functions, we exploit classical approximants going back to Euler and recently generalized in the light of the Trefftz-Fichera orthogonal invariants method. Working in multiple precision (up to 140 significant figures in decimal system), we compute explicit approximants obtaining more than 100 exact figures for the first positive zero. By inversion of this zero as a function of the order, we evaluate the first eigenvalue of the exponential potential Schrödinger operator with the same accuracy. 相似文献
6.
A. Varga 《International journal of control》2013,86(17):1712-1723
We present a numerical approach to evaluate the transfer function matrices of a periodic system corresponding to lifted state-space representations as constant systems. The proposed pole-zero method determines each entry of the transfer function matrix in a minimal zeros-poles-gain representation. A basic computation is the minimal realization of special single-input single-output periodic systems, for which both balancing-related as well as orthogonal periodic Kalman forms based algorithms can be employed. The main computational ingredient to compute poles is the extended periodic real Schur form of a periodic matrix. This form also underlies the solution of periodic Lyapunov equations when computing minimal realizations via balancing-related techniques. To compute zeros and gains, numerically stable fast algorithms are proposed, which are specially tailored to particular single-input single-output periodic systems. The new method relies exclusively on reliable numerical computations and is well suited for robust software implementations. Numerical examples computed with MATLAB-based implementations show the applicability of the proposed method to high-order periodic systems. 相似文献
7.
Let W be a simply connected region in , analytic in W and γ a positively oriented Jordan curve in W that does not pass through any zero of f. We present an algorithm for computing all the zeros of f that lie in the interior of γ. It proceeds by evaluating certain integrals along γ numerically and is based on the theory
of formal orthogonal polynomials. The algorithm requires only f and not its first derivative f'. We have found that it gives accurate approximations for the zeros. Moreover, it is self-starting in the sense that it does
not require initial approximations. The algorithm works for simple zeros as well as multiple zeros, although it is unable
to compute the multiplicity of a zero explicitly. Numerical examples illustrate the effectiveness of our approach.
Received: November 2, 1998; revised March 30, 1999 相似文献
8.
9.
David G. Meyer 《Automatica》1988,24(6)
Given a linear, time-invariant, discrete-time plant, we consider the optimal control problem of minimizing, by choice of a stabilizing compensator, the seminorm of a selected closed-loop map in a basic feedback system. The seminorm can be selected to reflect any chosen performance feature and must satisfy only a mild condition concerning finite impulse responses. We show that if the plant has no poles or zeros on the unit circle, then the calculation of the minimum achievable seminorm is equivalent to the maximization of a linear objective over a convex set in a low-dimensional Euclidean space. Hence, for a wide variety of optimal control problems, one can compute the answer to an infinite-dimensional optimization by a finite-dimensional procedure. This allows the use of effective numerical methods for computation. 相似文献
10.
LUCIANO PANDOLF 《International journal of control》2013,86(6):959-976
In this paper we study the properties of the zeros of a system with general delays in the input, state and control variables. The main result of this paper shows that the zeros of the transfer function are always zeros of the system matrix, with of at least the same multiplicity moreover, when the system is canonical, the zeros of the system matrix are zeros of the transfer function, with the same multiplicity. 相似文献
11.
A new characterization of system zeros of an arbitrary linear system described by a state-space model S(A, B, C, D) is presented. The transmission zeros are characterized as invariant zeros of an appropriate strictly proper system with a smaller number of inputs and outputs than the original system. The approach is based on singular value decomposition (SVD) of the first nonzero Markov parameter. This result together with characterization of invariant and decoupling zeros, based on the Moore-Penrose inverse of the first nonzero Markov parameter and the Kalman canonical decomposition theorem, provided in the first part of the paper yield a complete characterization of system zeros of an arbitrary multi-input/multi-output system 相似文献
12.
13.
R. V. PATEL 《International journal of systems science》2013,44(10):1171-1180
In this paper a numerical method is presented for computing the invariant zeros of a controllable linear, time-invariant, multivariable system described by the 4-tuplo (A, B, C, D) or the triple (A, B, C). The method is based on the fact. that a controllable system can be made maximally unobservable by means of state variable feedback, thereby causing the cancellation of the invariant zeros by an equal number of the system poles. The invariant zeros are obtained as the eigenvalues of a matrix of the same dimension as the number of invariant zeros. The method is applicable to both multivariable as well as single-input, single-output systems. Examples are given to illustrate the use of the method. 相似文献
14.
If a system with regular system pencil and relative degree greater than one is perturbed, the relative degree will typically decrease, and new finite zeros will appear. These new zeros are singularly perturbed. This paper applies a new canonical parameterization to systems with singular system pencils. Such systems have undefined relative degree. In singular systems, new zeros also appear under small perturbation, but they are not necessarily singularly perturbed. Rather, these zeros may appear at any frequency 相似文献
15.
O. A. SEBAKHY M. EL SINGABY I. F. EL ARABAWY 《International journal of systems science》2013,44(12):1741-1750
Based on an algorithm for computing the zeros of a linear multivariable system, we obtain a characterization of the number of zeros introduced by the squaring of the system as well as the locations of these zeros. The problem is shown to be closely related to that of pole assignment by output feedback. 相似文献
16.
The zeros of the discrete-time system obtained when sampling a continuous time system are explored. Theorems for the limiting zeros for large and small sampling periods are given. Conditions which guarantee that the sampled system has stable zeros are also presented. 相似文献
17.
A previous definition of transmission zeros of a system is refined to include multiple transmission zeros. 相似文献
18.
F. Svaricek 《Systems & Control Letters》1985,6(4):261-266
The structural invariants like finite and infinite zeros play an important role in many problems in the analysis of linear systems. In [1] Emami-Naeini and Van Dooren presented the program zeros for computing the finite zeros of a linear system, which in the author's opinion is at present the best commonly available program for this problem. Such a program does not exist for computing the other structural invariants, like the infinite zeros and the Kronecker indices. This paper presents an extended version of the program zeros, which computes the finite zeros as well as the other structural invariants. 相似文献
19.
This paper introduces the notion of input- (output-) decoupling structural zeros for linear time-invariant systems, described by Rosenbrock's system polynomial matrices. This notion is based on the definition of polynomial system matrices having the same structure that is given in this paper. Namely the input- (output-) decoupling structural zeros are decoupling zeros that are present for every choice of the system parameters. The main results are derived using digraph theory. An example illustrates the procedure for detecting structural zeros. 相似文献
20.
The zeros and the slope of the asymptotes to the root-loci of linear, passive, time-invariant systems are found. Using the geometric approach to the definition of zeros, it is proved that the system finite zeros are all in the left half of the complex plane and that the asymptotes to the system root-loci at infinity are all in the direction of the negative real axis. 相似文献