共查询到20条相似文献,搜索用时 15 毫秒
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V. P. Yakovets 《Ukrainian Mathematical Journal》1997,49(9):1442-1463
For a linear system of ordinary differential equations with degenerate matrix of derivatives, we find conditions of reducibility
to the central canonical form. We also establish the structure of the general solution and conditions of solvability of the
Cauchy problem, and study the problem of periodic solutions.
Nezhin Pedagogic Institute, Nezhin. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 9, pp. 1278–1296, September,
1997. 相似文献
3.
Shmuel Friedland 《Israel Journal of Mathematics》1980,35(1-2):89-108
LetA(ε) andB(ε) be complex valued matrices analytic in ε at the origin.A(ε)≈
p
B(ε) ifA(ε) is similar toB(ε) for any |ε|<r,A(ε)≈a
B(ε) ifB(ε)=T(ε)A(ε)T
−1(ε) andT(ε) is analytic and |T(ε)|≠0 for |ε|<r! In this paper we find a necessary and sufficient conditions onA(ε) andB(ε) such thatA(ε)≈
a
B(ε) provided thatA(ε)≈
p
B(ε). This problem arises in study of certain ordinary differential equations singular with respect to a parameter ε in the
origin and was first stated by Wasow.
Sponsored by the United States Army under Contract No. DAAG29-75-C-0024 相似文献
4.
L. Pandolfi 《Journal of Optimization Theory and Applications》1981,33(2):241-254
In this paper, we study the finite-time regulator problem for linear, autonomous, degenerate systems, i.e., systems described by the differential equation
with det(K)=0. Two investigations of the regulator problem are presented, which depend on the quadratic cost associated with the differential equation.This work was performed under the auspices of the National Research Council of Italy, Gruppo Nazionale per l'Analisi Funzionale e le Sue Applicazioni, Rome, Italy. 相似文献
5.
New sufficient conditions for the existence of invariant manifolds are proved for linear systems with degenerate matrix by the derivative.Translated from Ukrainskii Matematichesii Zhurnal, Vol. 45, No. 2, pp. 279–286, February, 1993. 相似文献
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A. A. Korobov 《Journal of Applied and Industrial Mathematics》2011,5(2):231-239
We prove the pointwise completeness of the order n system with constant coefficients under the assumption that the matrices of the system split into square blocks of the same
size so that the collection of all blocks embeds into a finite dimensional associative division algebra; the block rank of
the passive matrix is at most 2. 相似文献
8.
A. N. Malyshev 《Doklady Mathematics》2013,87(2):153-155
A novel numerical algorithm is proposed for solving systems of linear equations with block-Toeplitz narrow-banded matrices. Its arithmetical cost is about double of that of the block cyclic reduction. The backward roundoff error stability of the method guarantees its reliability for the matrices that are not symmetric positive definite or diagonally dominant. 相似文献
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In this paper we show that a complete characterization of the controllability property for linear control system on three-dimensional solvable nonnilpotent Lie groups is possible by the LARC and the knowledge of the eigenvalues of the derivation associated with the drift of the system. 相似文献
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A. Favini 《Applied Mathematics and Optimization》1980,6(1):153-167
Generalizations of well-known conditions for controllability of linear abstract autonomous systems defined on Banach spaces to the case where there is a closed non invertible operator at the derivative are established. Presence of this operator implies that suitable controllers must be chosen. If the operators entering in the equation satisfy certain hypotheses, approximate controllability by use of this class of controllers is expressed only in terms of the coefficients of the system. In particular, approximate controllability in finite time is then equivalent to approximate controllability, according to the usual definition, of a corresponding non degenerate system. This is the case, for example, when the concerned spaces are finite dimensional. Some applications to partial differential equations are given.This paper was written under the auspices of the Gruppo Nazionale per l'Analisi Funzionale e le sue Applicazioni of the Consiglio Nazionale delle Ricerche 相似文献
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Let denote the set of continuous n×n matrices on an interval . We say that is a nontrivial k-involution if where ζ=e-2πi/k, d0+d1++dk-1=n, and with . We say that is R-symmetric if R(t)A(t)R-1(t)=A(t), , and we show that if A is R-symmetric then solving x′=A(t)x or x′=A(t)x+f(t) reduces to solving k independent dℓ×dℓ systems, 0ℓk-1. We consider the asymptotic behavior of the solutions in the case where . Finally, we sketch analogous results for linear systems of difference equations. 相似文献
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Using the Lyapunov direct method, we establish a condition of exponential dichotomy for the class of dynamical systems under weaker assumptions as compared to the case of an arbitrary continuous matrix on the derivative of the Lyapunov function along the trajectories. By way of application, we obtain a sufficient condition for the dichotomy of a second order almost periodic vector equation in terms of coefficients. 相似文献
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Jiuping Xu Zhigao Liao Juan J. Nieto 《Journal of Mathematical Analysis and Applications》2010,368(1):54-68
This paper investigates the first order linear fuzzy differential dynamical systems with fuzzy matrices. We use a complex number representation of the α-level sets of the fuzzy system, and obtain the solution by employing such representation. It is applicable to practical computations and has also some implications for the theory of fuzzy differential equations. We then present some properties of the 2-dimensional dynamical systems and their phase portraits. Some examples are considered to show the richness of the theory and we can clearly see that new behaviors appear. We finally present some conclusions and new directions for further research in the area of fuzzy dynamical systems. 相似文献
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N. A. Izobov S. E. Karpovich L. G. Krasnevskii A. V. Lipnitskii 《Differential Equations》2008,44(12):1659-1672
For a linear nonstationary system with skew-symmetric continuously differentiable coefficient matrix of arbitrary even dimension, we construct its quasi-integrals and obtain effective coefficient estimates for their deviations from the corresponding integrals in the stationary case. For each trajectory of motion described by such a system and lying on the sphere of the corresponding radius, these estimates permit precisely indicating a domain on the sphere containing the trajectory on a nonsmall time interval. The estimates can also be used for expanding the multidimensional motion of a mechanical object into multicomponent elements of lower dimension. 相似文献
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V. I. Gel’fgat 《Computational Mathematics and Mathematical Physics》2013,53(8):1057-1061
Formulas for inverting nonsingular Toeplitz matrices with complex entries are derived. These formulas either refine known ones or are new. They make it possible to develop economical algorithms for calculating products of inverse Toeplitz matrices with vectors. 相似文献
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The solution of scheduling problems often gives rise to highly degenerate linear programmes which cause significant computational difficulties for the revised simplex method. Wolfe's highly effective ad hoc method for overcoming the cycling or stalling problems associated with degeneracy is described. Here it is given a geometric interpretation in terms of finding a direction of recession for a reduced problem which is fundamental to a full understanding of the procedure. An example of an aircrew scheduling problem is used to illustrate the effectiveness of the method. 相似文献