An improved method for estimating the domain of attraction of nonlinear systems containing rational functions

12th European Workshop on Advanced Control and Diagnosis

Polcz, Péter^1 ; Szederkényi, Gábor^1,2 ; Péni, Tamás^2

Faculty of Information Technology and Bionics, Pázmány Péter Catholic University, Práter u. 50/a, Budapest

H-1083, Hungary^1

Systems and Control Laboratory, Institute for Computer Science and Control (MTA SZTAKI), Hungarian Academy of Sciences, Kende u. 13-17, Budapest

H-1111, Hungary^2

关键词: Automatic modeling;    Computational problem;    Domain of attraction;    Linear Fractional Transformations;    LMI-condition;    Optimization based methods;    Quadratic form;    Rational terms;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/659/1/012038/pdf
DOI  :  10.1088/1742-6596/659/1/012038

来源: IOP

【 摘 要 】

An optimization based method is proposed in this paper for the computation of Lyapunov functions and regions of attractions for nonlinear systems containing polynomial and rational terms. The Lyapunov function is given in a special quadratic form, and the negativity of its derivative is ensured using appropriate LMI conditions. The conservatism of the solution is reduced by utilizing Finsler's lemma. The number of monomial and rational terms in the computational problem is kept as low as possible using linear fractional transformation (LFT) and automatic model simplification steps. The operation of the method is illustrated on two examples taken from the literature.