On low-noise modeling: a summary

Summary form only given. It has been affirmed that the observability indices of the pair H,F and the corresponding linear dependences of the rows of the observability matrix provide a parametrization of all solutions of the exact (noiseless) linear modeling problem. Additional constraints such as complexity or stability can also be taken care of in this framework. In the present work, an attempt is made to extend these results to the noisy case. If the noise is low, it is shown by A.C. Antoulas and B.D.O. Anderson (1992) how to define noisy versions of the observability indices and of the corresponding linear relationships of the rows of the observability matrix of the pair H,F, so that the results of the noiseless case are generalized. A criterion for the correct definition of these noisy quantities is that the noiseless results be recovered as the noise goes to zero