Stability domain estimation and design for nonlinear systems with bounded control inputs

Abstract

The problem of estimating robust stability domains for a class of nonlinear systems subject to actuator saturation is addressed. The unforced nonlinear system is represented by differential-algebraic equations which are linear with respect to the state and algebraic vectors, and the saturation nonlinearity is modelled by a sector bound condition. The system stability is analyzed by means of linear matrix inequality conditions based on non-quadratic Lyapunov functions. A non-saturated control strategy is also proposed in order to stabilize the system while maximizing the stability domain.