Control with exponentially decaying Lyapunov functions and its use for systems with input saturation

This paper presents a design method for feedback controls which leads to an exponentially decaying Lyapunov function for the closed-loop system. The rate of decay is the only and thus central parameter of the proposed design. The tight connection between the control law and the Lyapunov function is particularly favorable once the input saturation becomes active. In that case an analytic estimate for the domain of attraction is derived by using the Lyapunov function. Increasing the rate of decay decreases the size of the estimate. Hence the online variation of the rate of decay turns out to be a natural way for designing a variable-structure controller.