Lyapunov Functions for Second-Order Differential Inclusions: A Viability Approach
✍ Scribed by Luis Marco; José Alberto Murillo
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 135 KB
- Volume
- 262
- Category
- Article
- ISSN
- 0022-247X
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✦ Synopsis
In this paper the existence of Lyapunov functions for second-order differential inclusions is analyzed by using the methodology of the Viability Theory. A necessary assumption on the initial states and sufficient conditions for the existence of local and global Lyapunov functions are obtained. An application is also provided. 2001 Academic Press
📜 SIMILAR VOLUMES
In this paper we investigate the existence of mild solutions on an infinite interval for second order functional differential inclusions in Banach spaces. We shall make use of a theorem of Ma, which is an extension to multivalued maps on locally convex topological spaces of Schaefer's theorem.
We suppose that there is a lower solution ␥ and an upper solution  in the reversed order, and we obtain optimal conditions in f to assure the existence of a solution lying between  and ␥.
## Abstract In this paper, necessary and sufficient conditions are derived for the existence of a common quadra‐tic Lyapunov function for a finite number of stable second order linear time‐invariant systems. Copyright © 2002 John Wiley & Sons, Ltd.