×

Structural stability of linear discrete systems via the exponential dichotomy. (English) Zbl 0661.93060

The authors of the paper show that the difference equation is structurally stable if and only if it has an exponential dichotomy.
Reviewer: V.Krakhatko

MSC:

93D99 Stability of control systems
93C05 Linear systems in control theory
93C55 Discrete-time control/observation systems
39A11 Stability of difference equations (MSC2000)
34D30 Structural stability and analogous concepts of solutions to ordinary differential equations
39A12 Discrete version of topics in analysis
PDF BibTeX XML Cite
Full Text: EuDML

References:

[1] W. A. Coppel: Stability and Asymptotic Behaviour of Differential Equations. Heath. Boston, 1965. · Zbl 0154.09301
[2] W. A. Coppel: Dichotomies in Stability Theory. Lecture Notes in Mathematics, No. 629, Springer Verlag, Berlin, 1978. · Zbl 0376.34001
[3] D. Henry: Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Mathematics, No. 840, Springer-Verlag, Berlin, 1981. · Zbl 0456.35001
[4] K. J. Palmer: A characterization of exponential dichotomy in terms of topological equivalence. J. Math. Anal. Appl. 69 (1979), 8-16. · Zbl 0419.34011
[5] K. J. Palmer: The structurally stable linear systems on the half-line are those with exponential dichotomies. J. Differential Equations, 33 (1979), 16-25. · Zbl 0378.34040
[6] G. Papaschinopoulos, J. Schinas: Criteria for an exponential dichotomy of difference equations. Czechoslovak Math. J. 35 (110) 1985, 295-299. · Zbl 0693.39001
[7] G. Papaschinopoulos, J. Schinas: A criterion for the exponential dichotomy of difference equations. Rend. Sem. Fac. Sci. Univ. Cagliari, Vol. 54, fasc. 1 (1984), 61-71. · Zbl 0607.39001
[8] G. Papaschinopoulos, J. Schinas: Multiplicative separation, diagonalizability and structural stability of linear difference equations. Differential Equations: Qualitative theory (Szeged 1984), Colloq. Math. Soc. János Bolyai, 47, North-Holland, Amsterdam-New York. · Zbl 0638.34047
[9] G. Papaschinopoulos: Exponential separation, exponential dichotomy and almost periodicity of linear difference equations. J. Math. Anal. Appl. 120 (1986), 276-287. · Zbl 0602.39001
[10] G. Papaschinopoulos, J. Schinas: Structural stability via the density of a class of linear discrete systems. J. Math. Anal. Appl. · Zbl 0628.39001
[11] J. Schinas, G. Papaschinopoulos: Topological equivalence for linear discrete systems via dichotomies and Lyapunov functions. Boll. Un. Math. Ital. 6, 4 (1985), 61 - 70. · Zbl 0579.39004
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.