Discrete time immersion and invariance adaptive control for systems in strict feedback form

This paper presents a new design procedure for the adaptive stabilization (regulation) via state feedback for discrete-time nonlinear systems in parametric strict-feedback form. The algorithm utilizes discrete-time adaptive backstepping in the controller construction together with a new method for the parameter estimator design. This approach provides a recursive construction which guarantees boundness of the closed-loop trajectories and global convergence to the origin of the state of the closed-loop system. The performance of the proposed method are illustrated by simulations.