Robust Adaptive Stabilization of Discrete-time First-order Systems

An algorithm for the adaptive stabilization of single-input single-output time-varying first-order discrete-time systems is presented. Only the knowledge of the sign of the feedback gain and an upper bound of it is required. The adaptive control law is robust with respect to nonlinear additive time-varying state, input and output perturbations. If the sign of the feedback gain is not known, it is shown that a simple modification of the control law leads to a controller which produces an asymptotically stable closed-loop system