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dc.contributor.author | Leela, S. | en |
dc.contributor.author | Lakshmikantham, V. | en |
dc.contributor.author | Oguztoreli, M. N. | en |
dc.date.accessioned | 2010-06-02T20:20:28Z | en |
dc.date.available | 2010-06-02T20:20:28Z | en |
dc.date.issued | 1980-02 | en |
dc.identifier.uri | http://hdl.handle.net/10106/2237 | en |
dc.description.abstract | **Please note that the full text is embargoed** ABSTRACT: It is now well known that the method of vector Lyapunov functions provides an effective tool to investigate the properties of large scale
interconnected dynamical and control systems. [3,4,5,11-15]. Several Lyapunov functions result in a natural way in the study of such systems by the decomposition and aggregation method [1-4,12-14]. However an unpleasant fact in this approach is the requirement of quasi-monotone property on the comparison system since comparison systems with a desired property like stability exist without satisfying quasi-monotone property. Also in the
study of comparison theorems and extremal solutions for differential systems one usually imposes this quasi-monotone property. To avoid this difficulty two ideas are suggested recently, namely to use an appropriate cone other than [see pdf for notation] and to exploit the new notion of quasi-solutions
[6,9,10], In [8] the idea of quasi-solutions is developed to some extent. In this paper we obtain further results on quasi-solutions. We introduce the notion of coupled quasi-solutions in addition to quasi-solutions. We show how the idea of quasi-solutions leads to isolated subsystems, obtain error estimates between solutions and quasi-solutions and develop monotone iterative techniques to obtain coupled maximal and minimal quasi-solutions. | en |
dc.language.iso | en_US | en |
dc.publisher | University of Texas at Arlington | en |
dc.relation.ispartofseries | Technical Report;125 | en |
dc.subject | Coupled quasi-solutions | en |
dc.subject | Control systems | en |
dc.subject | Error estimates | en |
dc.subject | Lyapunov functions | en |
dc.subject.lcsh | Mathematics Research | en |
dc.title | Quasi-Solutions, Vector Lyapunov Functions and Monotone Method | en |
dc.type | Technical Report | en |
dc.publisher.department | Department of Mathematics | en |
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