Data-driven output regulation by external models of linear hybrid systems with periodic jumps

In this paper, the robust output regulation problem for linear hybrid systems in the presence of periodic jumps is considered. The solution is provided in terms of an External Model, as opposed to the classical implementation of an Internal Model, providing a suitable steady-state signal to the pre-stabilized plant. The construction of the External Model does not rely on the exact knowledge of any value defining the plant or its interconnection with the exosystem and it is based merely on input-output data. The design consists essentially in two different phases: firstly, the steady-state relation between the output error and the state of the External Model unit is estimated by means of input-output measurements, and, second, such estimate is exploited to suitably update the state of the External Model in order to generate the correct steady-state signal achieving regulation, in such a way that the original asymptotic stability property of the plant is not affected by the reset mechanism.