Ill-posedness and Ill-conditioning in the use of CARMA, CARIMA and Box-Jenkins models in identification and control

The paper discusses applicability of CARMA, CARIMA and Box-Jenkins models for identification of systems of different structure. Especially, the difficulties encountered by unstable plant modes are considered. It is shown that the behaviour of identification algorithms may depend on location of the noise in the real system. Therefore it may be advisable to use different models for identification purposes for the two cases when the noise is known to affect the input or the output of the system. It is also shown that the use of CARIMA model for modeling of systems which do not exhibit Brownian motion noises may lead to numerical difficulties in control design.