Prior knowledge and Markov parameters of linear time-invariant models

The subspace-based state-space system identification techniques have been applied to different industrial applications with success for more than two decades [36, 10, 4, 1, 8, 27, 7, 14]. A quick look at these contributions leads to the conclusion that these accurate results are mainly obtained with collected measurements of good quality. It is now well-known that using persistently exciting inputs (of sufficiently high order) is compulsory in order to get a reliable estimated model [34, 22, 37]. Like any standard identification method, the subspace-based identification algorithms require the verification of specific excitation constraints in order to verify particular rank conditions and to ensure the consistency of the subspace estimates [16, 9]. Unfortunately, in many practical situations, these excitation constraints are difficult to be satisfied because they may involve experimental conditions not conceivable for economical and/or safety reasons. Such a poor experimental framework often leads to a small amount of measurement samples corrupted by noise with a low signal-noise-ratio. This lack of information (due to the poor excitation of the system) should be improved by adding prior knowledge about the system into the identification procedure [32]. Indeed, it is common for the operator to have prior information concerning the process to be identified, e.g., from