Characterizations of Generalized Exponential Trichotomies for Linear Discrete-time Systems

Popa, Ioan-Lucian; Ceauşu, Traian; Bagdasar, Ovidiu; Agarwal, Ravi P.

doi:10.2478/auom-2019-0025

Abstract

The concept of generalized exponential trichotomy for linear time-varying systems is investigated in relationship with the classical notion of uniform exponential trichotomy. Some key properties of generalized exponential trichotomy are explored through supplementary projections. These results are also extended to the case of projection sequences, while certain applications for adjoint systems are suggested.

References

[1] A.I. Alonso, J. Hong, R. Obaya, Exponential dichotomy and trichotomy for difference equations, Comput. Math. Appl. Vol. 38 (1999), 41-49.10.1016/S0898-1221(99)00167-4
Search in Google Scholar Back to article
[2] A. Castaneda, G. Robledo, A Topological Equivalence Result for a Family of Nonlinear Difference Systems Having Generalized Exponential Dichotomy, J. Difference Equ. Appl., DOI:10.1080/10236198.2016.119216110.1080/10236198.2016.1192161
Open DOI Search in Google Scholar Back to article
[3] L. Dingjun, W. Xian, Z. Deming, H. Maoan, Bifurcation Theory and Methods od Dynamical Systems, Advenced Series in Dynamical Systems, Vol. 15, World Scientific, 1997
Search in Google Scholar Back to article
[4] A. Ducrot, P. Magal, O. Seydi, Persistence of Exponential Trichotomy for Linear Operators: A Lyapunov-Perron Approach, J. Dynam. Differential Equations, Vol. 28 (2016), 93-126.10.1007/s10884-015-9493-3
Search in Google Scholar Back to article
[5] S. Elaydi, K. Janglajew, Dichotomy and Trichotomy of Difference Equations, J. Difference Equ. Appl. Vol. 3 (1998), 417-448.10.1080/10236199708808113
Search in Google Scholar Back to article
[6] N. Lupa, M. Megan, Generalized exponential trichotomies for abstract evolution operators on the real line, J. Funct. Spaces Appl., Vol. 2013, Article ID 409049, 8 pages, 2013.10.1155/2013/409049
Search in Google Scholar Back to article
[7] C.L. Mihit, M. Megan, T. Ceausu, The Equivalence of Datko and Lyapunov Properties for (h,k)-Trichotomic Linear Discrete-Time Systems, Discrete Dyn. Nat. Soc. Volume 2016, Article ID 3760262, 8 pages10.1155/2016/3760262
Search in Google Scholar Back to article
[8] G. Papaschinopoulos, A Linearization result for a differential equation with piecewise constant argument, Analysis, 16 (1996), 161-170.10.1524/anly.1996.16.2.161
Search in Google Scholar Back to article
[9] G. Papaschinopoulos, On exponential trichotomy of linear difference equations Appl. Anal. 40 (1991), 89-109.10.1080/00036819108839996
Search in Google Scholar Back to article
[10] I.-L. Popa, T. Ceausu, Generalized exponential trichotomy for difference equations, IEEE 11th International Symposium on Applied Computational Intelligence and Informatics, 2016, 173-176.10.1109/SACI.2016.7507357
Search in Google Scholar Back to article
[11] I.-L. Popa, T. Ceauşu, O. Bagdasar, Characterizations of generalized exponential trichotomies for linear discrete-time systems, Electron. Notes Discrete Math., 56 (2016), 7-13.10.1016/j.endm.2016.11.002
Search in Google Scholar Back to article
[12] I.-L. Popa, M. Megan, T. Ceauşu, On h-Trichotomy of Linear Discrete-Time Systems in Banach Spaces, Acta Univ. Aplulensis Ser. Mat. Inf., 39 (2014), 329-339.10.17114/j.aua.2014.39.28
Search in Google Scholar Back to article
[13] I.-L. Popa, T. Ceauşu, M. Megan, Characterizations of the (h, k, μ, ν)−Trichotomy for Linear Time-Varying Systems, Math. Methods Appl. Sci., 40 (17), 2016, 6172-6177.10.1002/mma.3907
Search in Google Scholar Back to article
[14] C. Vidal, C. Cuevas, Wighted Exponential Trichotomy of Linear Differential Equations, Proceedings of the Conference on Differential & Difference Equations and Applications, 2006, 1077-1086.
Search in Google Scholar Back to article
[15] Z.-G. Li, X.-Q. Song, X.-L. Yang, On nonuniform polynomial trichotomy of linear discrete-time systems in Banach spaces, J. Appl. Math., vol. 2014, Article ID 807265, 6 pages, 2014.10.1155/2014/807265
Search in Google Scholar Back to article

Characterizations of Generalized Exponential Trichotomies for Linear Discrete-time Systems

Abstract

Paradigm

My account