A measurement of multivariable interaction in mastery of the time and of the frequency

In this paper we consider the analysis of multiple-input multiple-output systems using the Participation Matrix, which provides a tool both for interaction measure and controller structure selection. For this matrix we present novel interpretations in the time and in the frequency domain, based on definition of Hilbert-Schmidt-Hankel norm. Moreover, the time domain interpretation is exploited to obtain an empirical estimate of the participation matrix directly from input-output data of the multivariable system.