On the estimation of the domain of attraction for saturated systems via partitioning of the input space

This paper revisits the problem of estimating the domain of attraction for systems with saturation nonlinearities. We divide the input space into several regions. In one of these regions, none of the inputs saturate. In each of the remaining regions, there is a unique input that saturates everywhere with the time-derivative of its saturated signal being zero. These special properties of the inputs in different regions of the input space are combined with an existing piecewise quadratic Lyapunov functions that contains the information of input saturation to arrive at a set of less conservative stability conditions, from which a larger level set of the piecewise quadratic Lyapunov function can be obtained as an estimate of the domain of attraction. Simulation results indicate that the proposed approach has the ability to obtain a significantly larger estimate of the domain of attraction than the existing methods.