Leírás
Authors: Péter Polcz, Gábor Szederkényi, Tamás Péni
In this contribution, we consider locally asymptotically stable nonlinear autonomous models in ODE form, where the coordinates functions of the right hand side are rational functions of the differential variables and may contain constant uncertain parameters. It is assumed that the initial values and the uncertain parameters belong to known polytopes. The rational terms contained in the Lyapunov function are computed using the linear fractional representation (LFR), and the required properties of the Lyapunov function are given in the form of linear matrix inequalities. The domain of attraction (DOA) is approximated using the appropriate level sets of the computed Lyapunov function. To add further degrees of freedom to the computations, we use Finsler's lemma, which requires the determination of affine annihilators for the basis functions. To decrease the size of the resulting optimization problem without increasing the level of conservatism of the DOA estimation, we propose simplification algorithms for the LFR and for the annihilator. The operation of the method is shown on illustrative examples known from the literature.
[1] P. Polcz, T. Péni and G. Szederkényi. Improved algorithm for computing
the domain of attraction of rational nonlinear systems. European Journal
of Control, 39:53-67, 2018.
[2] P. Polcz, T. Péni and G. Szederkényi. Reduced linear fractional
representation of nonlinear systems for stability analysis. IFAC Papers
Online, 51:37-42, 2018.