Global Exponential Stabilization and Global Lp Performance of a Saturated Double Integrator

This letter presents novel results on the simultaneous global internal and external stabilization problem for the double integrator controlled by a saturated staticstate linear feedback. The methodology capitalizes on thedistinctive characteristics of the smooth strictly increasing saturation function considered to strengthen and extendthe stability properties reported in the existing literature for this canonical system. Concretely, as the maincontributions, this letter demonstrates that the resulting closed-loop system, in the absence of disturbances, is globally exponentially stable and, in the face of non-inputadditive disturbances, is globally L-p stable for any given p is an element of [1,infinity) and yields a bounded state trajectory. The simulation experiments showcase these new findings