Determination of robust asymptotic stability of nonlinear systems by Ehlich and Zeller method

In this master's thesis, the method developed by Ehlich and Zeller, along with second-degree Lyapunov functions, was utilized to determine stability regions. This method actually satisfies necessary and sufficient conditions characterizing the regions considered as asymptotically stable regions around stable equilibrium points. This technique has been applied to nonlinear systems with polynomial structures in this master's study. In the study, a numerical approach utilizing second-degree Lyapunov functions and the necessary and sufficient conditions obtained with the method proposed by Ehlich and Zeller has been suggested. With this approach, an attempt has been made to obtain the maximum stability region around the equilibrium point x^*= 0. To achieve this, as many second-degree Lyapunov functions as possible have been utilized. To find the maximum stability region, the union of stability regions obtained from each Lyapunov function has been taken. The proposed method defines a kind of optimization problem for nonlinear systems with polynomial structures and involves its numerical solution. The main feature of this approach is the ability to find the maximum stability region achievable for the selected second-degree Lyapunov function.