On hyperexponential stabilization of a chain of integrators in continuous and discrete time subject to unmatched perturbations

A recursive time-varying state feedback is presented for a chain of integrators with unmatched perturbations in continuous and discrete time. In continuous time, it is shown that hyperexponential convergence is achieved for the first state variable $x_1$, while the second state $x_2$ remains bounded. For the other states, we establish ISS {\cb property} by saturating the growing {\cb control} gain. In discrete time, we use implicit Euler discretization to {\cb preserve} hyperexponential convergence. The main results are demonstrated through several examples of the proposed control laws, illustrating the conditions established for both continuous and discrete-time systems.