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Source Publication Title

Technical Report 125


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.


Mathematics | Physical Sciences and Mathematics

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Mathematics Commons



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