On the Estimation of Robust Stability Regions for Nonlinear Systems with Saturation

This paper addresses the problem of determining robust stability regions for a class of nonlinear systems with timeinvariant uncertainties subject to actuator saturation. The unforced nonlinear system is represented by differentialalgebraic equations where the system matrices are allowed to be rational functions of the state and uncertain parameters, and the saturation nonlinearity is modelled by a sector bound condition. For this class of systems, local stability conditions in terms of linear matrix inequalities are derived based on polynomial Lyapunov functions in which the Lyapunov matrix is a quadratic function of the state and uncertain parameters. To estimate a robust stability region is considered the largest level surface of the Lyapunov function belonging to a given polytopic region of state. A numerical example is used to demonstrate the approach.