Three counterexamples to recent results on finite- and fixed-time convergent controllers and observers

Recent results regarding the stability properties of an extended super-twisting controller, the convergence of smooth finite- and fixed-time convergent differentiators, and an upper convergence time bound for a homogeneous state-feedback control law are revisited. Counterexamples show that three such results are incorrect as stated. New formal results obtained in course of the examples’ construction and their discussion provide valuable insight into the considered controllers and observers.