@article{Liu:2012aa,
    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.},
    Author = {Liu, Jiang and Zhan, Naijun and Zhao, Hengjun},
    Date = {2012/12/01},
    File = {Automatically Discovering Relaxed Lyapunov Functions for Polynomial Dynamical Systems - liu2012 - a.pdf},
    ISBN = {1661-8289},
    Journal = {Mathematics in Computer Science},
    Number = {4},
    Pages = {395--408},
    Title = {Automatically Discovering Relaxed Lyapunov Functions for Polynomial Dynamical Systems},
    URL = {https://doi.org/10.1007/s11786-012-0133-6},
    Volume = {6},
    Year = {2012},
    bdsk-url-1 = {https://doi.org/10.1007/s11786-012-0133-6},
    date-added = {2023-04-18 07:32:40 +0200},
    date-modified = {2023-04-18 07:32:40 +0200},
    id = {Liu2012},
    doi = {10.1007/s11786-012-0133-6}
}

@article{Liu:2012aa, 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.}, Author = {Liu, Jiang and Zhan, Naijun and Zhao, Hengjun}, Date = {2012/12/01}, File = {Automatically Discovering Relaxed Lyapunov Functions for Polynomial Dynamical Systems - liu2012 - a.pdf}, ISBN = {1661-8289}, Journal = {Mathematics in Computer Science}, Number = {4}, Pages = {395--408}, Title = {Automatically Discovering Relaxed Lyapunov Functions for Polynomial Dynamical Systems}, URL = {https://doi.org/10.1007/s11786-012-0133-6}, Volume = {6}, Year = {2012}, bdsk-url-1 = {https://doi.org/10.1007/s11786-012-0133-6}, date-added = {2023-04-18 07:32:40 +0200}, date-modified = {2023-04-18 07:32:40 +0200}, id = {Liu2012}, doi = {10.1007/s11786-012-0133-6} }