  Maximum likelihood identification of linear time-invariant models is a
difficult problem because it is, in general, a nonlinear semidefinite program,
with semidefinite covariance matrix arguments and semidefinite filter stability
constraints. To enforce filter stability, we establish a general theory of
closed constraints on the system eigenvalues using LMI regions. To solve the
identification problem, we employ a Cholesky factorization method that reduces
the semidefinite program to a standard nonlinear program. Finally, we apply the
identification algorithm to a class of linear plant and disturbance models
commonly used in offset-free model predictive control applications.
Specifically, we consider models that are structured with uncontrollable,
integrating disturbance states. We solve this disturbance modeling problem, and
validate the resulting controller and estimator performance, in two real-world
case studies: first, a low-cost benchmark temperature control laboratory, and
second, an industrial-scale chemical reactor at Eastman Chemical's Kingsport
plant.
