Discrete system order reduction using multipoint step response matching (Q596221)

The transfer function of a reduced model for a known higher-order discrete-time system is written in partial fraction form with poles \(\lambda_i\) and residues \(\alpha_i\). The constant term (residue at \(\infty\)) is obtained by matching the steady state of the given system. The remaining parameters \(\alpha_i\) and \(\lambda_i\) are found by matching the unit step response of the given system at \(2r\) (\(r\) is the order of the reduced system) time instances suitably spread over the transient region. When translated in the \(z\)-domain, this leads to a system of \(2r\) nonlinear equations that is solved by Newton's method.