  This paper extends the concept of scalar cepstrum coefficients from
single-input single-output linear time invariant dynamical systems to
multiple-input multiple-output models, making use of the Smith-McMillan form of
the transfer function. These coefficients are interpreted in terms of poles and
transmission zeros of the underlying dynamical system. We present a method to
compute the MIMO cepstrum based on input/output signal data for systems with
square transfer function matrices (i.e. systems with as many inputs as
outputs). This allows us to do a model-free analysis. Two examples to
illustrate these results are included: a simple MIMO system with 3 inputs and 3
outputs, of which the poles and zeros are known exactly, that allows us to
directly verify the equivalences derived in the paper, and a case study on
realistic data. This case study analyses data coming from a (model of) a
non-isothermal continuous stirred tank reactor, which experiences linear
fouling. We analyse normal and faulty operating behaviour, both with and
without a controller present. We show that the cepstrum detects faulty
behaviour, even when hidden by controller compensation. The code for the
numerical analysis is available online.
