Operations Research Transactions >
2023 , Vol. 27 >Issue 4: 20 - 32
DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2023.04.002
S-lemma and its extension
Received date: 2023-04-28
Online published: 2023-12-07
S-lemma is an important theorem in operations research and cybernetics. In this paper, starting from verifying the global asymptotic stability of a nonlinear control system, we draw S-procedure, S-lemma, and their relations and differences. Then the basic content of S-lemma and its latest advances are introduced. Moreover, several generalizations of S-lemma over the complex field and the quaternion set are discussed. Finally, some basic results corresponding to S-lemma are showed for any number of symmetric (or Hermitian) matrices.
Key words： S-procedure; S-lemma; Yuan's lemma; low-rank solutions
Wenbao AI, Wei LIANG, Mengxiao ZHANG . S-lemma and its extension[J]. Operations Research Transactions, 2023 , 27(4) : 20 -32 . DOI: 10.15960/j.cnki.issn.1007-6093.2023.04.002
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