Closed-loop identification of MIMO systems: a new look at identifiability and experiment design

This paper addresses a question raised by a leading expert in the identification of multivariable systems: “Is it necessary to excite all reference signals for the identification of a multivariable system operating in closed loop with a linear time-invariant controller?” On the basis of earlier results on identifiability of closed-loop systems, he conjectured that this was necessary. We show that it is not, on the basis of a careful re-examination of the notions of identifiability and informative experiments for closed-loop systems.