General formulation of a Prony based method for simultaneous identification of transfer functions and initial conditions

Previous results on transfer function identification using Prony signal analysis methods are extended. The class of allowed input signals is expanded: the signals can exhibit jump discontinuities and can be characterized by a finite number of eigenvalues between discontinuities. The advantage of this more general input form is that it can be tailored to excite system modes in frequency ranges of interest. In addition to generating system eigenvalues and transfer function residues, the approach can be used to obtain a feedthrough gain and initial condition residues. The approach makes maximum use of available input-output data during each phase of the solution. For the first phase of the solution, in which system eigenvalues are estimated, several alternative approaches are described. For the second phase of the solution, all available data are used in determining estimates of transfer function residues and initial condition residues. Methods of model order selection also are described, and a detailed example is given to illustrate the approach