SIFAT-SIFAT SPEKTRAL DAN STRUKTUR KOMBINATORIK PADA SISTEM POSITIF 2D
Keywords:
Finite Memory, 2D positive system, Separability, property L, Spectral properties
Abstract
The dynamics of a 2D positive system depends on the pair of nonnegative square matrices that
provide the updating of its local states. In this paper, several spectral properties, like finite
memory, separablility and property L, which depend on the characteristic polynomial of the
pair, are investigated under the nonnegativity constraint and in connection with the
combinatorial structure of the matrices.
Some aspects of the Perron-Frobenius theory are extended to the 2D case; in particular,
conditions are provided guaranteeing the existence of a common maximal eigenvector for two
nonnegative matrices with irreducible sum. Finally, some results on 2D positive realizations
are presented
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Theory, Van Nostrand Reinhold, New York
Bisiacco, M., 1985, State and output feedback
stabilizability of 2D systems, IEEE Trans. Circ.
Sys., vol CAS-32, pp. 1246-54.
Cullen, C.G., 1966, Matrices and Linear
Transformations, Addison-Wesley Publising
Company.
Davis P.J,1979, Circulant Matrices, John Wiley & Sons.
Drazin, M.P, 1950, Some generalizations of matrix
commutativity, Proc. London Math. Soc.,(3),1, 222-
31.
Fornasini,E. and Machesini,G., 1976, State-Space
Realization Theory Of Two-Demensional Filters,
IEEE Trans.Aut.Contr,vol.AC-21,484-492.
Fornasini,E. and Machesini,G., 1978, Doubly-Indexed
Dynamical systems : State-Space Models and
Tructural Properties, Math.Systems .Teory, vol. 12,
59-72.
Fornasini,E. and Machesini,G., 1993, 2D state dynamics
and geometry of the matrix pairs, in multivariate
Analysis, Future Directions, C.R. Rao ed., Elsevier
Sci.Publ.,pp. 131-53.
Fornasini,E., Marchesini,G., and Valcher,M.E., 1994, On
The Structure of Finite Memory and Separable Two-
Dimensional Systems, Automatica, vol. 30, 347-350.
Fornasini,E., and Valcher,M.E.,1994, Matrix Pairs in
Two-Dimensional Systems : an Approach Based on
Trace Series an Hankel Matrices, to appear in SIAM
J. Contr.Opt.
Fornasini,E., 1991, A 2D systems approach to river
pollution modelling, Multid. Sys. Sign. Process., 2,
pp.233-65
Frank Ayres, 1974, Theory and Problems of Matrices,
McGraw-Hill, Inc.
Grantmacher, F.R., 1960, The Theory of Matrices,
Chelsea Pub.Co., Vol. 2
Gilbert W.J., 1976, Modern Algebra With Applications,
John Wiley & Sons.
Luenberger, D.G., Introduction to dynamical systems, J.
Wiley & Sons Inc., 1979.
Motzkin,T.S., and Taussky,O., 1952, Pairs of Matrices
With property L(1), Trans.Amer.Scc., vol.73. 108-
114.
Orlob, G.T,. 1983, Mathematical Modeling of Water
Quality: Steams, Lakes, dan Reservoirs,
International Institute for Applied Systems Analysis.
Soehakso,R.M.J.T., Teori Graph, Diktat .Kuliah MIPA
UGM.
Valcher,M.E., and Fornasini,E., 1994, State Models and Asymptotic Behavior of Two-Dimensional Positive Systems, to Appear in IMA J. of Appl.Math.
Varga, R.S., 1962, Matrix Iterative Analysis, Prentice-Hall, inc.
Published
2011-03-01
How to Cite
[1]
R. MATAKUPAN, “SIFAT-SIFAT SPEKTRAL DAN STRUKTUR KOMBINATORIK PADA SISTEM POSITIF 2D”, BAREKENG: J. Math. & App., vol. 5, no. 1, pp. 21-27, Mar. 2011.
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