Output regulation for non-square multi-rate systems

We address the problem of regulating a subset of outputs of a linear time-invariant plant with multi-rate measurements so as to achieve asymptotic tracking of an exogenous signal generated by the free motion of a linear time-invariant system, denoted by exosystem. A solution to this problem is required to yield closed-loop stability and should be such that output regulation is achieved even in the presence of small plant uncertainties and exogenous disturbances also generated by the exosystem. Contrarily to previous works, we propose a solution to the general case where the plant may have more measured outputs than inputs. We show that this solution allows us to solve simultaneous stabilization and output regulation problems that are not possible to solve through the previous works. Besides incorporating an internal model of the exosystem, the key feature of our proposed controller is that it includes a system that blocks signals generated by the exosystem arriving to the controller from the non-regulated outputs.