Notes on data-driven output-feedback control of linear MIMO systems

Recent works have approached the data-driven design of dynamic output-feedback controllers for discrete-time LTI systems by constructing non-minimal state vectors composed of past inputs and outputs. Depending on the system’s complexity (order $n$, lag $\mathrm{\ell }$ and number of outputs $p$), it was observed in several works that such an approach presents significant limitations. In particular, many works require to restrict the class of LTI systems to those satisfying the relation $p\mathrm{\ell }=n$. In this note, we show how to address the general MIMO case (for which $p\mathrm{\ell }\ge n$ in general) by constructing an alternative non-minimal state vector from data. Different from the existing literature, our method guarantees the satisfaction of certain rank conditions when the system is persistently excited, thereby facilitating the direct data-driven dynamic output-feedback control of MIMO systems by applying methods that were originally developed for the input-state data setting.