On Equivalence of Data Informativity for Identification and Data-Driven Control of Partially Observable Systems

This study shows that the informativity for the identification of partially observable systems is equivalent to that for designing dynamical measurement-feedback stabilizers. This finding is entirely different from the input-state case, where the direct data-driven design of state-feedback stabilizers requires less informativity than system identification. We derive the equivalence between the two types of informativity based on a newly introduced vector autoregressive with exogenous input (VARX) framework, which is suitable for time-domain analyses, such as state-space models, while directly representing input–output characteristics, such as transfer functions. Moreover, we show a duality between the characterization of all VARX models explaining data and that of all VARX controllers stabilizing such VARX models.