Reducing the complexity of the sum-of-squares test for stability of delayed linear systems

Yashun Zhang, Matthew Peet, Keqin Gu

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


This technical note considers the problem of reducing the computational complexity associated with the Sum-of-Squares approach to stability analysis of time-delay systems. Specifically, this technical note considers systems with a large state-space but where delays affect only certain parts of the system. This yields a coefficient matrix of the delayed state with low ranka common scenario in practice. The technical note uses the general framework of coupled differential-difference equations with delays in feedback channels. This framework includes systems of both the neutral and retarded-type. The approach is based on recent results which introduced a new LyapunovKrasovskii structure which was shown to be necessary and sufficient for stability of this class of systems. This technical note shows how exploiting the structure of the new functional can yield dramatic improvements in computational complexity. Numerical examples are given to illustrate this improvement.

Original languageEnglish (US)
Article number5605235
Pages (from-to)229-234
Number of pages6
JournalIEEE Transactions on Automatic Control
Issue number1
StatePublished - Jan 2011
Externally publishedYes


  • Complexity
  • LyapunovKrasovskii functional
  • semi definite programming
  • sum-of-squares
  • time delay

ASJC Scopus subject areas

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


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