Abstract
We advocate a type of expresions for the fundamental matrix of linear singularly perturbed systems which allow to consider various stability questions as well as applications to some nonlinear problems, to Ito equations, to degenerate situations, and in control problems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Gradstein, I.S., On behaviour of solutions of systems of linear differential equations degenerating in the limit, Doklady Akad. Nauk SSSR (N.S.), 53, 391–394 (1946), (Russian).
Tihonov A.N., On the dependence of the solutions of differentilal equations on a small parameter, Mat.Sbornik (N.S.), 22(64), 193–204(1948).
Levin, J.J.; Levinson, N., Singular perturbations of nonlinear systems of differential equations and an associated boundary layer equation, J.Rational Mech.Anal., vol.3, no.2, 247–270(1954).
Vasilieva, A.B.; Butuzov, V.F., Asymptotic expansions of solutions of singularly perturbed equations, (Russian), Nauka, Moscow, 1973.
Wasow, W., Asymptotic expansions for ordinary differential equations, Interscience, John Wiley, New York, 1965.
O’Malley, R.E., Jr., Introduction to singular perturbations, Academic Press, 1974.
Klimušev, A.I.; Krasovski, N.N., Uniform asymptotic stability of systems of differential equations with small parameters multiplying the derivatives, (Russian), Prikl.Mat.Mech.T.25 (1961), 680–690.
Gradstein, I.S., On the solutions on the time half axis of differential equations with small parameters multiplying the derivatives (Russian), Mat.Sbornik T.32, (74) no.3(1953), 680–690.
DrĂgan, V.; Halanay, A., Stability problems for synchronous machines by singular perturbations methods, Revue Roumaine Sci. Techniques, Electrotechnique et Energétique, vol.27, no.2(1982).
DrĂgan, V., A new case in the hybrid control of nonstationary systems with fast transients, Revue Roumaine Sci.Techniques, Electrotechnique et Energétique, vol.26, no.3(1981), 447–453.
DrĂgan, V.; Halanay, A., Suboptimal stabilization of linear systems with several true scales, Int.J.Control, (1982), vo.36, no.1, 109–126.
DrĂgan, V.; Halanay, A., Perturbaţii singulare, DezvoltĂri asimptotice, Editura Academiei R.S.R. (in preparation).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1983 Springer-Verlag
About this paper
Cite this paper
DrĂgan, V., Halanay, A. (1983). Uniform asymptotic expresions for the fundamental matrix of singularly perturbed linear systems and applications. In: Verhulst, F. (eds) Asymptotic Analysis II —. Lecture Notes in Mathematics, vol 985. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062369
Download citation
DOI: https://doi.org/10.1007/BFb0062369
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-12286-9
Online ISBN: 978-3-540-39612-3
eBook Packages: Springer Book Archive