Abstract
This paper deals with the identification of linear constant dynamical systems when formalized as a rational approximation problem. The criterion is the l 2 norm of the transfer function, which is of interest in a stochastic context. The problem can be expressed as nonlinear optimization in a Hilbert space, but standard algorithms are usually not well adapted. We present a generic recursive procedure to find a local optimum of the criterion in the case of scalar systems. Our methods are borrowed from differential theory mixed with a bit of classical complex analysis. To our knowledge, the algorithm described in this paper is the first that ensures convergence to a local minimum.
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