On Stability and Gain Convergence in Discrete Simple Adaptive Control

Successful implementations of simple direct adaptive control techniques in various domains of application have been presented over the last two decades in the technical literature. The theoretical background concerning basic conditions needed for stability of the controller and the open questions relating the convergence of the adaptive gains have been recently clarified, yet only for the continuous-time algorithms. Apparently, asymptotic tracking in discrete time systems is possible only with step input commands and the scope of the so called “almost strictly positive real” condition is also not clear. This paper expands the feasibility of discrete simple adaptive control methodology to include any desired input commands and almost all real-world systems. The proofs of stability are also rigorously revised.