  This paper introduces a dual input-output parameterization (dual IOP) for the
identification of linear time-invariant systems from closed-loop data. It draws
inspiration from the recent input-output parameterization developed to
synthesize a stabilizing controller. The controller is parameterized in terms
of closed-loop transfer functions, from the external disturbances to the input
and output of the system, constrained to lie in a given subspace. Analogously,
the dual IOP method parameterizes the unknown plant with analogous closed-loop
transfer functions, also referred to as dual parameters. In this case, these
closed-loop transfer functions are constrained to lie in an affine subspace
guaranteeing that the identified plant is \emph{stabilized} by the known
controller. Compared with existing closed-loop identification techniques
guaranteeing closed-loop stability, such as the dual Youla parameterization,
the dual IOP neither requires a doubly-coprime factorization of the controller
nor a nominal plant that is stabilized by the controller. The dual IOP does not
depend on the order and the state-space realization of the controller either,
as in the dual system-level parameterization. Simulation shows that the dual
IOP outperforms the existing benchmark methods.
