A numerical method for the stability analysis of quasi-polynomial vector fields (Q1863610)

A quasi-polynomial (QP) system is defined by the equations \[ \dot x=\ell_ix_i+x_i\sum_{j=1}^m A_{ij}\prod_{k=1}^n x_k^{B_{jk}},\quad i=1,\dots,n,\quad x\in \mathbb{R}^n,\tag{*} \] where \(B=[B_{ij}]\) and \(A=[A_{ij}]\) are constant real matrices. The number \(m\) is related to the number of quasi-monomials in the vector field of (\(*\)). Sufficient conditions for the existence of a Lyapunov function in the class of (QP) dynamical systems are derived. When the system parameters are numerically specified, a numerical algorithm is used which involves the resolution of a linear matrix inequality.