Robust Domain of Attraction Estimates for a Class of Uncertain Discrete-Time Nonlinear Systems*

This paper proposes a linear matrix inequality based method to the estimation of a robust domain of attraction for a class of discrete-time nonlinear systems subject to uncertain constant parameters. Recursive algebraic representations of the system dynamics and of the Lyapunov stability conditions are applied to obtain convex conditions which guarantee the system robust local stability while providing an estimate of the domain of attraction. A large class of discrete-time nonlinear systems and of Lyapunov functions can be embedded in the proposed methodology including the whole class of regular rational functions of the system state variable and uncertain parameters. A numerical example illustrates the application of the proposed method.