Quasi-Solutions, Vector Lyapunov Functions and Monotone Method

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Quasi-Solutions, Vector Lyapunov Functions and Monotone Method

Show simple item record Leela, S. en Lakshmikantham, V. en Oguztoreli, M. N. en 2010-06-02T20:20:28Z en 2010-06-02T20:20:28Z en 1980-02 en
dc.identifier.uri en
dc.description.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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