Generalized S-procedure for inequality conditions on one-vector-lossless sets and linear system analysis

Yoshio Ebihara, Katsutoshi Maeda, Tomomichi Hagiwara

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


The generalized version of the S-procedure, recently introduced by Iwasaki and co-authors and Scherer independently, has proved to be very useful for robustness analysis and synthesis of control systems. In particular, this procedure provides a nonconservative way to convert specific inequality conditions on lossless sets into numerically verifiable conditions represented by linear matrix inequalities (LMIs). In this paper, we introduce a new notion, one-vector-lossless sets, and propose a generalized S-procedure to reduce inequality conditions on one-vector-lossless sets into LMIs without any conservatism. By means of the proposed generalized S-procedure, we can examine various properties of matrix-valued functions over some regions on the complex plane. To illustrate the usefulness, we show that full rank property analysis problems of polynomial matrices over some specific regions on the complex plane can be reduced into LMI feasibility problems. It turns out that many existing results such as Lyapunov's inequalities and LMIs for state-feedback controller synthesis readily follow from the suggested generalized S-procedure.

Original languageEnglish
Pages (from-to)1547-1555
Number of pages9
JournalSIAM Journal on Control and Optimization
Issue number3
Publication statusPublished - 2008
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Applied Mathematics


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