Optimal Hankel-Norm Model Reductions: Multivariable Systems

Sun Yuan Kung, David W. Lin

Research output: Contribution to journalArticlepeer-review

221 Scopus citations


This paper represents a first attempt to derive a closed-form (Hankel-norm) optimal solution for multivariable system reduction problems. The basic idea is to extend the scalar case approach in [5] to deal with the mulrivariable systems. The major contribution lies in the development of a minimal degree approximation (MDA) theorem and a computation algorithm. The main theorem describes a closed-form formulation for the optimal approximants, with the optimality verified by a complete error analysis. In deriving the main theorem, some useful singular value/vector properties associated with block-Hankel matrices are explored and a key extension theorem is also developed. Imbedded in the polynomial-theoretic derivation of the extension theorem is an efficient approximation algorithm. This algorithm consists of three steps: i) compute the minimal basis solution of a polynomial matrix equation; ii) solve an algebraic Riccati equation; and iii) find the partial fraction expansion of a rational matrix.

Original languageEnglish (US)
Pages (from-to)832-852
Number of pages21
JournalIEEE Transactions on Automatic Control
Issue number4
StatePublished - Aug 1981
Externally publishedYes

All Science Journal Classification (ASJC) codes

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


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