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.
Categories: eess.SY cs.SY