On the Simultaneous Identification of Transfer Functions and Initial Conditions

Methods are developed to obtain continuous system eigenvalues and residues along with initial condition residues. The system may have a feedforward gain, and the output of the system may include a constant offset. The identification is based on periodically sampled input and output values. Depending on the nature of the input signal between sampling instants, two sets of relationships are derived. In both cases, a weighted least-squares method is used to obtain optimal coefficients of three z-transform polynomials. Expressions for initial condition residues and continuous system transfer-function residues are developed in terms of the three polynomials. The transfer function part of the solution is shown to be independent of the initial condition part.