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.
ASJC Scopus subject areas
- Physics and Astronomy(all)