DYNAMIC SISO AND MISO SYSTEM APPROXIMATIONS BASED ON OPTIMAL LAGUERREMODELS

A general procedure, based on the knowledge of the input and the outpu t signals, is proposed to approximate the prescribed linear time-invar iant (LTI) systems by means of optimal Laguerre models. The main contr ibution of this paper is to apply the Newton Raphson's iterative techn ique to compute the so-called optimal Laguerre pole in a continuous-ti me case (or optimal time scale factor in a discrete-time case) and esp ecially to show that the gradient and the Hessian can be expressed ana lytically. Moreover, the excitations used are not limited to the ones that ensure the orthogonality of the outputs of Laguerre filters (i.e. , Dirac delta or white noise) as is usually done in existing methods, however persislently exciting input signal(s) are used. The proposed p rocedure will be directly formulated for multi-input/single-output (MI SO) systems, single-input/single-output (SISO) systems being a special case with the number of inputs equal to one. The proposed algorithm h as direct applications in system identification, model reduction, and noisy modeling.