Robust adaptive control of linear discrete-time systems with rapidly-varying parameters

In this paper an indirect adaptive regulator is constructed for single-input single-output linear time-varying discrete-time systems. The plant parameters are modeled as a linear combination of known bounded functions which may be fast varying with unknown slowly-varying coefficients that are confined to a convex set. The unknown coefficients are estimated using a gradient type estimator with a projection operation. It is assumed that the system is uniformly N-step reachable, where N is an integer greater than or equal to the system dimension. It is then shown that the resulting closed-loop system is globally stable for a sufficiently small rate of the unknown variations. This adaptive regulator is also shown to be robust to disturbances and/or small model errors