Show simple item record

dc.contributor.authorDragan, Vasile ( Orcid Icon 0000-0001-6617-1441 )
dc.contributor.authorFreiling, Gerhard ( )
dc.contributor.authorHochhaus, Andreas ( )
dc.contributor.authorMorozan, Toader ( )
dc.date.accessioned2021-04-26T19:07:51Z
dc.date.available2021-04-26T19:07:51Z
dc.date.issued2004-08-06
dc.identifier.citationDragan, V., Freiling, G., Hochhaus, A., & Morozan, T. (2004). A class of nonlinear differential equations on the space of symmetric matrices. Electronic Journal of Differential Equations, 2004(96), pp. 1-48.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/13450
dc.description.abstractIn the first part of this paper we analyze the properties of the evolution operators of linear differential equations generating a positive evolution and provide a set of conditions which characterize the exponential stability of the zero solution, which extend the classical theory of Lyapunov. In the main part of this work we prove a monotonicity and a comparison theorem for the solutions of a class of time-varying rational matrix differential equations arising from stochastic control and derive existence and (in the periodic case) convergence results for the solutions. The results obtained are similar to those known for matrix Riccati differential equations. Moreover we provide necessary and sufficient conditions which guarantee the existence of some special solutions for the considered nonlinear differential equations as: maximal solution, stabilizing solution, minimal positive semi-definite solution. In particular it turns out that under the assumption that the underlying system satisfies adequate generalized stabilizability, detectability and definiteness conditions there exists a unique stabilizing solution.en_US
dc.formatText
dc.format.extent47 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherSouthwest Texas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2004, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectRational matrix differential equationsen_US
dc.subjectGeneralized Riccati differential equationsen_US
dc.subjectGeneralized stabilizability and detectabilityen_US
dc.subjectComparison theoremen_US
dc.subjectExistence and convergence resultsen_US
dc.titleA class of nonlinear differential equations on the space of symmetric matricesen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


Download

Thumbnail

This item appears in the following Collection(s)

Show simple item record