Discrete-time model reference adaptive control for continuous-time systems using generalized sampled-data hold functions

The generalized sampled-data hold functions approach of P.T. Kabamba (1987) is extended to the control of linear time-invariant systems with unknown parameters. The idea of Kabamba´s approach is to periodically sample the plant output and define the control as the sampled output plus a discrete-time reference, each multiplied by an individual modulating function. Such a control makes it possible to assign an arbitrary discrete-time transfer function for the sampled closed-loop system and does not make assumptions on the plant other than controllability and observability. The authors propose an indirect adaptive controller which is based on this approach and estimates the modulating functions online. In particular, the control is modified so that persistent excitation of the continuous-time plant is ensured without making an assumption on the reference signal, and discrete-time asymptotic model-following is nevertheless obtained. The only assumptions on the plant are minimality, for the continuous and sampled plant, and known order