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1.
A condition for a polynomial p(s) to be a local convex direction for a Hurwitz stable polynomial q(s) is derived. The condition is in terms of polynomials associated with the even and odd parts of p(s) and q ( s), and constitutes a generalization of Rantzer's phase-growth condition for global convex directions. It is used to determine convex directions for certain subsets of Hurwitz stable polynomials 相似文献
2.
The characterization of convex direction for real Hurwitz matrices is extended to the case of multivariable time delay linear systems. The above is achieved using the results of convex directions for quasipolynomials. An illustrative example is given. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
3.
In some important applications, such as the edge-theorem, it is required that a polynomial is α-stable along a parameter segment. Using the critical constraint, the necessary and sufficient conditions for root clustering (α-stability) of convex combinations of complex polynomials are presented. The approach is general and requires that a certain real polynomial has no zeros in the open interval (0,1) 相似文献
4.
José Herskovits Wilhelm P. Freire Mario Tanaka Fo Alfredo Canelas 《Structural and Multidisciplinary Optimization》2011,44(3):363-377
We propose a new technique for minimization of convex functions not necessarily smooth. Our approach employs an equivalent
constrained optimization problem and approximated linear programs obtained with cutting planes. At each iteration a search
direction and a step length are computed. If the step length is considered “non serious”, a cutting plane is added and a new
search direction is computed. This procedure is repeated until a “serious” step is obtained. When this happens, the search
direction is a feasible descent direction of the constrained equivalent problem. To compute the search directions we employ
the same formulation as in FDIPA, the Feasible Directions Interior Point Algorithm for constrained optimization. We prove
global convergence of the present method. A set of numerical tests is described. The present technique was also successfully
applied to the topology optimization of robust trusses. Our results are comparable to those obtained with other well known
established methods. 相似文献
5.
We show an equivalence between conditions for linear systems to be stabilizable by stable controllers and conditions for convex combinations of polynomials to be stable 相似文献
6.
Constructing simple stable descriptions for image partitioning 总被引:6,自引:2,他引:4
Yvan G. Leclerc 《International Journal of Computer Vision》1989,3(1):73-102
7.
Djaferis T.E. Pepyne D.L. Cushing D.M. 《Automatic Control, IEEE Transactions on》2002,47(9):1546-1550
In this note, we develop a new characterization of stable polynomials. Specifically, given n positive, ordered numbers (frequencies), we develop a procedure for constructing a stable degree n monic polynomial with real coefficients. This construction can be viewed as a mapping from the space of n ordered frequencies to the space of stable degree n monic polynomials. The mapping is one-one and onto, thereby giving a complete parameterization of all stable, degree n monic polynomials. We show how the result can be used to generate parameterizations of stabilizing fixed-order proper controllers for unity feedback systems. We apply these results in the development of stability margin lower bounds for systems with parameter uncertainty. 相似文献
8.
The first half of this paper introducesEpsilon Geometry, a framework for the development of robust geometric algorithms using inaccurate primitives. Epsilon Geometry is based on a very general model of imprecise computations, which includes floating-point and rounded-integer arithmetic as special cases. The second half of the paper introduces the notion of a (–)-convex polygon, a polygon that remains convex even if its vertices are all arbitrarily displaced by a distance of of less, and proves some interesting properties of such polygons. In particular, we prove that for every point set there exists a (–)-convex polygonH such that every point is at most 4 away fromH. Using the tools of Epsilon Geometry, we develop robust algorithms for testing whether a polygon is (–)-convex, for testing whether a point is inside a (–)-convex polygon, and for computing a (–)-convex approximate hull for a set of points. 相似文献
9.
One useful generalization of the convex hull of a setS ofn points is the ?-strongly convex δ-hull. It is defined to be a convex polygon with vertices taken fromS such that no point inS lies farther than δ outside and such that even if the vertices of are perturbed by as much as ?, remains convex. It was an open question as to whether an ?-strongly convexO(?)-hull existed for all positive ?. We give here anO(n logn) algorithm for constructing it (which thus proves its existence). This algorithm uses exact rational arithmetic. We also show how to construct an ?-strongly convexO(? + μ)-hull inO(n logn) time using rounded arithmetic with rounding unit μ. This is the first rounded-arithmetic convex-hull algorithm which guarantees a convex output and which has error independent ofn. 相似文献
10.
One useful generalization of the convex hull of a setS ofn points is the -strongly convex -hull. It is defined to be a convex polygon with vertices taken fromS such that no point inS lies farther than outside and such that even if the vertices of are perturbed by as much as , remains convex. It was an open question as to whether an -strongly convexO()-hull existed for all positive . We give here anO(n logn) algorithm for constructing it (which thus proves its existence). This algorithm uses exact rational arithmetic. We also show how to construct an -strongly convexO( + )-hull inO(n logn) time using rounded arithmetic with rounding unit . This is the first rounded-arithmetic convex-hull algorithm which guarantees a convex output and which has error independent ofn. 相似文献
11.
A new numerical method, based on hybrid of Block-pulse and Legendre polynomials for numerical evaluation of Hankel transform is proposed in this paper. Hybrid of Block-pulse and Legendre polynomials are used as a basis to expand a part of the integrand, rf(r), appearing in the Hankel transform integral. Thus transforming the integral into a Fourier-Bessel series. Truncating the series, an efficient algorithm is obtained for the numerical evaluations of the Hankel transforms of order ν>−1. The method is quite accurate and stable, as illustrated by given numerical examples with varying degree of random noise terms εθi added to the data function f(r), where θi is a uniform random variable with values in [−1,1]. Finally, an application of the proposed method is given in solving the heat equation in an infinite cylinder with a radiation condition. 相似文献
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14.
Exploiting spectral properties of symmetric banded Toeplitz matrices, we describe simple sufficient conditions for the positivity of a trigonometric polynomial formulated as linear matrix inequalities (LMIs) in the coefficients. As an application of these results, we derive a hierarchy of convex LMI inner approximations (affine sections of the cone of positive definite matrices of size m) of the nonconvex set of Schur stable polynomials of given degree n<m. It is shown that when m tends to infinity the hierarchy converges to a lifted LMI approximation (projection of an LMI set defined in a lifted space of dimension quadratic in n) already studied in the technical literature. An application to robust controller design is described. 相似文献
15.
A. A. Nesenchuk 《Automation and Remote Control》2010,71(8):1515-1525
The problem of synthesis of an asymptotically stable polynomial on the basis of the initial unstable polynomial is solved.
For the purpose of its solution, the notion of the extended (complete) root locus of a polynomial is introduced, which enables
one to observe the dynamics of all its coefficients simultaneously, to isolate the root-locus trajectories, along which values
of each coefficient change, to establish their interrelation, which provides a way of using these trajectories as “conductors”
for the movement of roots in the desired domains. Values of the coefficients that ensure the stability of a polynomial are
chosen from the stability intervals found on the stated trajectories as the nearest values to the values of appropriate coefficients
of the unstable polynomial or by any other criterion, for example, the criterion of provision of the required stability reserve.
The sphere of application of the root locus, which is conventionally used for synthesis of characteristic polynomials through
the variation of only one parameter (coefficient) of the polynomial, is extended for the synthesis of polynomials by way of
changing all coefficients and with many changing coefficients. Examples of application of the developed algorithm are considered
for the synthesis of stable polynomials with constant and interval coefficients. 相似文献
16.
Choon Ki Ahn 《Computers & Mathematics with Applications》2012,63(5):887-895
In this paper, we propose some new results on stability for Takagi–Sugeno fuzzy delayed neural networks with a stable learning method. Based on the Lyapunov–Krasovskii approach, for the first time, a new learning method is presented to not only guarantee the exponential stability of Takagi–Sugeno fuzzy neural networks with time-delay, but also reduce the effect of external disturbance to a prescribed attenuation level. The proposed learning method can be obtained by solving a convex optimization problem which is represented in terms of a set of linear matrix inequalities (LMIs). An illustrative example is given to demonstrate the effectiveness of the proposed learning method. 相似文献
17.
In expert systems and other applications of logic programming, the issue arises of whether to use rules for forward or backward inference, i.e. whether deduction should be driven by the facts available to the program or the questions that are put to it. Often some mixture of the two is cheaper than using either mode exclusively.We show that, under two restrictive assumptions, optimal choices of directions for the rules can be made in time polynomial in the number of rules in the system. If we abandon one of these restrictions, the optimal choice is NP-complete. Search methods are presented which allow graceful degradation from polynomial time to exponential time.The cost estimates on which the optimisation is based are also discussed. The methods used to estimate costs fail when recursion is present in the rules, thus limiting the set of logic programs to which this optimisation can be applied.This work was supported by the Office of Naval Research, the National Institute of Health, and Martin-Marietta under contracts N00014-81-K-0004, NIH 5P41 RR 00785, and GH3-116803 相似文献
18.
HereR andN denote respectively the real numbers and the nonnegative integers. Also 0 <n εN, ands(x) =x
1+...+x
n when x = (x
1,...,x
n) εR
n. Adiagonal function of dimensionn is a mapf onN
n (or any larger set) that takesN
n bijectively ontoN and, for all x, y inN
n, hasf(x) <f(y) whenevers(x) <s(y). We show that diagonalpolynomials f of dimensionn all have total degreen and have the same terms of that degree, so that the lower-degree terms characterize any suchf. We call two polynomialsequivalent if relabeling variables makes them identical. Then, up to equivalence, dimension two admits just one diagonal polynomial,
and dimension three admits just two. 相似文献
19.
In this paper, new results concerning the factorizability of multidimensional polynomials are presented. Necessary and sufficient conditions for the factorizability or separation of a givenm -D (m - dimensional) polynomial into: 1)m 1-D polynomials, and 2) a number of multidimensional polynomials of appropriate dimensions are explicitly formulated. 相似文献
20.
《Journal of Symbolic Computation》2005,39(1):103-126
An algorithm to compute a good basis of the Brieskorn lattice of a cohomologically tame polynomial is described. This algorithm is based on the results of C. Sabbah and generalizes the algorithm by A. Douai for convenient Newton non-degenerate polynomials. 相似文献