A necessary and sufficient minimality condition for uncertain systems

Carolyn L. Beck, John Doyle

Research output: Contribution to journalArticlepeer-review


A necessary and sufficient condition is given for the exact reduction of systems modeled by linear fractional transformations (LFT's) on structured operator sets. This condition is based on the existence of a rank-deficient solution to either of a pair of linear matrix inequalities which generalize Lyapunov equations; the notion of Gramians is thus also generalized to uncertain systems, as well as Kalman-like decomposition structures. A related minimality condition, the converse of the reducibility condition, may then be inferred from these results and the equivalence class of all minimal LFT realizations defined. These results comprise the first stage of a complete generalization of realization theory concepts to uncertain systems. Subsequent results, such as the definition of and rank tests on structured controllability and observability matrices are also given. The minimality results described herein are applicable to multidimensional system realizations as well as to uncertain systems; connections to formal powers series representations also exist.

Original languageEnglish (US)
Pages (from-to)1802-1813
Number of pages12
JournalIEEE Transactions on Automatic Control
Issue number10
StatePublished - Oct 1999


  • Minimality
  • Model reduction
  • Uncertain systems

ASJC Scopus subject areas

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


Dive into the research topics of 'A necessary and sufficient minimality condition for uncertain systems'. Together they form a unique fingerprint.

Cite this