Routh Approximations for Reducing Order of Linear, Time-Invariant Systems

Maurice F. Hutton, Bernard Friedland

Research output: Contribution to journalArticlepeer-review

533 Scopus citations


A new method of approximating the transfer function of a high-order linear system by one of lower order is proposed. Called the “Routh approximation method” because it is based on an expansion that uses the Routh table of the original transfer function, the method has a number of useful properties: if the original transfer function is stable, then all approximants are stable; the sequence of approximants converge monotonically to the original in terms of “impulse response” energy; the approximants are partial Padé approximants in the sense that the first k coefficients of the power series expansions of the kth-order approximant and of the original are equal; the poles and zeros of the approximants move toward the poles and zeros of the original as the order of the approximation is increased. A numerical example is given for the calculation of the Routh approximants of a fourth-order transfer function and for illustration of some of the properties.

Original languageEnglish (US)
Pages (from-to)329-337
Number of pages9
JournalIEEE Transactions on Automatic Control
Issue number3
StatePublished - Jun 1975
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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