抄録
In this paper, we study system identification in H∞ norm using fractional representation of rational function and propose several algorithms. Model sets considered here are discrete time systems and available data are the finite series of input/output signals where initial conditions are zero. Evaluated functions used in the algorithms are coprime factors errors of a plant and its model and they are related to graph metric or gap metric. We show two methods to give the normalized coprime factorizations of the plants or the models: state space representation method using Riccati equation and Cholesky decomposition method with Toeplitz matrices. The high order coefficients of the error functions in time shift operator are unknown because data are finite. In this paper, the unknown coefficients are optimally interpolated in H∞ norm and we give the lower bounds of the errors. Through the numerical examples we show that the series of functions which are not continuous in the sense of the graph topology can be sensitively identified by the proposed methods.
