Local Stability Analysis of Saturating Systems via Polynomial Programming

This paper considers the local stability analysis of feedback systems with saturation nonlinearities. First, considering the detailed structure of the saturation nonlinearity, we derive a local stability condition with the aid of S-Procedure of polynomial with higher degrees of freedom. Then, we obtain a Lyapunov function using Sum of Squares decomposition. Furthermore, it is shown that this method can be easily extended to the case where piecewise quadratic Lyapunov functions are adopted. Finally we demonstrate its effectiveness through numerical examples.