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.