A new method to estimate a guaranteed subset of the domain of attraction for non-polynomial systems

We will present a new method to estimate the guaranteed subset of the domain of attraction (DOA) around an asymptotically stable equilibrium for time invariant, autonomous and non-polynomial systems. The presented method is based on Lyapunov´s stability theory, the theorem of Ehlich and Zeller and the univariate interval Newton method. Without calculating the polynomial interpolation of the non-polynomials, we compute a lower and upper bound for the interpolation error for each of the non-polynomial terms. Then, the theorem of Ehlich and Zeller can be adapted to non-polynomial systems using the interpolation error bound. For a given quadratic Lyapunov function (QLF), an upper and lower bound for the guaranteed DOA is calculated. The effectiveness of the presented method will be illustrated by two examples.