Block diagonalization of systems with measurable coefficients
DOI:
https://doi.org/10.22199/S07160917.1994.0001.00002Keywords:
Diagonalization of linear systems, Systems with Carathéodory conditionsAbstract
In this paper we show that, previous results given by Coppel concerning the existence of projection matrix P, and a change of variable x = S(t)y reducing system x = A(t)x, where A(t) is a continuous matrix function, to the form y= A(t)y, with the property P A(t) = A(t)P, can be extended to the case when A(t) is a locally integrable function.
References
[1] Agarwal, R.P., Difference Equations and lnequalities, Pure and Aplied Mathematics, Marcel Dekker, New York, 1992.
[2] Bainov, D.D., Simeonov, P.S., Systems with Impulse Effect, Ellis Horwood and John Wiley, New York, 1989
[3] Coddington E., Levinson N., Theory of Ordinary Differential Equations, McGraw Hill, New York, 1955.
[4] Cooke, K., Asymptotic theory for the delay differential equation, ul = -au(t-r(t)), J. Math. An. and App., Vol. 19, 1, pp. 160-173, 1967.
[5] Coppel W.A., Dichotomies and reducibility, Journal of differential equations 3. 500-.521, (1967).
[6] Coppel W.A., Dichotomies in Stability Theory, Lectures Notes in Mathematics, 629, Springer-Verlag, Berlin, 1978.
[7] Kreyszing E., Introductory Functional Analysis with Applications, John Wiley, New York, 1978.
[8] Lee E., Markus L., Foundations of Optimal Control Theory, John Wiley and Sons, New York, 1967.
[9] Naulin R., Dichotomies for systems with unbounded coefficients, IMA, UCV, Valparaíso, 1992 (Preprint).
[10] Naulin, R., Pinto, M., Block diagonalization of linear impulsive systems, Facultad de Ciencias, Universidad de Chile, 1 992(preprint).
[11] Palmer, K., Exponential dichotomies and transversal homoclinic points, J. Diff. Eqns., 55, pp. 22.5-256, 1984.
[12] Prodi G., Ambrosetti A., Analisi non Lineare, 1 Quaderno, Scuola Normale Superiore, Pisa, 1973.
[2] Bainov, D.D., Simeonov, P.S., Systems with Impulse Effect, Ellis Horwood and John Wiley, New York, 1989
[3] Coddington E., Levinson N., Theory of Ordinary Differential Equations, McGraw Hill, New York, 1955.
[4] Cooke, K., Asymptotic theory for the delay differential equation, ul = -au(t-r(t)), J. Math. An. and App., Vol. 19, 1, pp. 160-173, 1967.
[5] Coppel W.A., Dichotomies and reducibility, Journal of differential equations 3. 500-.521, (1967).
[6] Coppel W.A., Dichotomies in Stability Theory, Lectures Notes in Mathematics, 629, Springer-Verlag, Berlin, 1978.
[7] Kreyszing E., Introductory Functional Analysis with Applications, John Wiley, New York, 1978.
[8] Lee E., Markus L., Foundations of Optimal Control Theory, John Wiley and Sons, New York, 1967.
[9] Naulin R., Dichotomies for systems with unbounded coefficients, IMA, UCV, Valparaíso, 1992 (Preprint).
[10] Naulin, R., Pinto, M., Block diagonalization of linear impulsive systems, Facultad de Ciencias, Universidad de Chile, 1 992(preprint).
[11] Palmer, K., Exponential dichotomies and transversal homoclinic points, J. Diff. Eqns., 55, pp. 22.5-256, 1984.
[12] Prodi G., Ambrosetti A., Analisi non Lineare, 1 Quaderno, Scuola Normale Superiore, Pisa, 1973.
Published
2018-04-03
How to Cite
[1]
R. Naulin, “Block diagonalization of systems with measurable coefficients”, Proyecciones (Antofagasta, On line), vol. 13, no. 1, pp. 01-07, Apr. 2018.
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