Conjugate convex Lyapunov functions for dual linear differential inclusions
Conjugate convex Lyapunov functions for dual linear differential inclusions
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DOI：
10.1109/tac.2006.872764
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发表时间：
2006-04
影响因子：
6.8
通讯作者：
R. Goebel;A. Teel;T. Hu;Zongli Lin
中科院分区：
文献类型：
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作者：
R. Goebel;A. Teel;T. Hu;Zongli Lin
凸分析工具用于显示稳定性属性和李亚普诺夫不等式在从线性微分包含 (LDI) 转换为对偶时如何转换。特别地，证明了凸正定函数是 LDI 的 Lyapunov 函数当且仅当其凸共轭是 LDI 对偶的 Lyapunov 函数。示例表明，这种二元性如何有效地使可用于评估 LDI 稳定性的工具数量增加一倍。
Tools from convex analysis are used to show how stability properties and Lyapunov inequalities translate when passing from a linear differential inclusion (LDI) to its dual. In particular, it is proved that a convex, positive definite function is a Lyapunov function for an LDI if and only if its convex conjugate is a Lyapunov function for the LDIs dual. Examples show how such duality effectively doubles the number of tools available for assessing stability of LDIs.