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Automatically Discovering Relaxed Lyapunov Functions for Polynomial Dynamical Systems |
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| Authors: | Jiang Liu Naijun Zhan Hengjun Zhao |
| Institution: | 1. Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, Building B, HON KWOW Center No. 85 Jinyu Avenue, North Zone, Chongqing, 401122, People’s Republic of China 2. State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, No. 4 South Fourth Street, Zhong Guan Cun, Beijing, 100190, People’s Republic of China 3. State key Laboratory of Computer Science, Institute of Software, University of Chinese Academy of Science, Chinese Academy of Sciences, No. 4 South Fourth Street, Zhong Guan Cun, Beijing, 100190, People’s Republic of China |
| Abstract: | The notion of Lyapunov function plays a key role in the design and verification of dynamical systems, as well as hybrid and cyber-physical systems. In this paper, to analyze the asymptotic stability of a dynamical system, we generalize standard Lyapunov functions to relaxed Lyapunov functions (RLFs), by considering higher order Lie derivatives. Furthermore, we present a method for automatically discovering polynomial RLFs for polynomial dynamical systems (PDSs). Our method is relatively complete in the sense that it is able to discover all polynomial RLFs with a given predefined template for any PDS. Therefore it can also generate all polynomial RLFs for the PDS by enumerating all polynomial templates. |
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