Model matching via multirate sampling with fast sampled input guaranteeing the stability of the plant zeros: extensions to adaptive control

The model matching problem in discrete systems with free-design zeros of the reference model for any fractional order-hold and a wide set of admissible values of the running sampling period used in the discretisation process of a linear and time-invariant single-input single-output continuous-time plant is investigated. A fast input sampling rate at sufficiently small sampling period is used with an appropriate set of scalar gains to generate the input sequence within the slow-running sampling period. This makes it possible to stabilise the discrete plant zeros that allows their cancellation in the model-matching problem synthesis irrespective of either the absence of continuous-time zeros or the presence of continuous-time critically stable or unstable ones. The design is extended to adaptive control for the case of unknown plants.