Geometric control of input saturated systems with guaranteed closed-loop performance and stability

We study the issue of stability of input constrained closed-loop systems with a class of differential geometric controllers. Specifically, a Lyapunov function-based method is presented for determining the closed-loop stability under geometric control laws for single-input single-output systems. This method provides a subset of the domain of attraction for guaranteed stability of the closed-loop system. Furthermore, it offers flexibility in adjusting the closed-loop performance while ensuring closed-loop stability in the presence of input saturation. Hence, by using this framework the designer can a posteriori verify overall stability of the closed-loop system for a desired closed-loop performance