Conditions for the equivalence of ARMAX and ARX systems

It is shown that an autoregressive moving average with exogenous input (ARMAX) system can be represented as an autoregressive with exogenous input (ARX) model if and only if the polynomial matrix corresponding to the moving average (MA) part of the system does not drop rank. A construction using the matrix fractional description of the system is used to prove this result. This construction shows that accurate ARX parameter estimates of systems driven by unmeasured disturbances can often be obtained by proper addition of sensor measurements and extending the order of the ARX model.<
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