Estimating the robust domain of attraction for non-smooth systems using an interval Lyapunov equation

Abstract

The Lyapunov equation allows finding a quadratic Lyapunov function for an asymptotically stable fixed point of a linear system. Applying this equation to the linearization of a nonlinear system can also prove the exponential stability of its fixed points. This paper proposes an interval version of the Lyapunov equation, which allows investigating a given Lyapunov candidate function for non-smooth nonlinear systems inside an explicitly given neighborhood, leading to rigorous estimates of the domain of attraction (EDA) of exponentially stable fixed points. These results are developed in the context of uncertain systems. Experiments are presented, which show the interest of the approach including with respect to usual approaches based on sum-of-squares for the computation of EDA.