TY - GEN
T1 - Symmetric formulation of the Kalman-Yakubovich-Popov lemma and exact losslessness condition
AU - Tanaka, Takashi
AU - Langbort, Cedric
PY - 2011
Y1 - 2011
N2 - This paper presents a new algebraic framework for robust stability analysis of linear time invariant systems with an emphasis on symmetry. The main motivation for this work is to provide a unified theory to answer when the the KYP lemma provides an exact LMI test for robust stability. The notions of weak and strong mutual losslessness are introduced to characterize for lossless S-procedures and the KYP lemma. The new framework has sufficient flexibility to unify some recent extensions of the KYP lemma, including the Generalized KYP lemma for finite frequency analysis, the KYP lemma for nD systems, and the diagonal KYP lemma for positive systems. Finally, we show that the new theory also suggests that the structured singular value of internally positive systems with arbitrary number of scalar uncertainties can be exactly computed.
AB - This paper presents a new algebraic framework for robust stability analysis of linear time invariant systems with an emphasis on symmetry. The main motivation for this work is to provide a unified theory to answer when the the KYP lemma provides an exact LMI test for robust stability. The notions of weak and strong mutual losslessness are introduced to characterize for lossless S-procedures and the KYP lemma. The new framework has sufficient flexibility to unify some recent extensions of the KYP lemma, including the Generalized KYP lemma for finite frequency analysis, the KYP lemma for nD systems, and the diagonal KYP lemma for positive systems. Finally, we show that the new theory also suggests that the structured singular value of internally positive systems with arbitrary number of scalar uncertainties can be exactly computed.
UR - http://www.scopus.com/inward/record.url?scp=84860692078&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84860692078&partnerID=8YFLogxK
U2 - 10.1109/CDC.2011.6160932
DO - 10.1109/CDC.2011.6160932
M3 - Conference contribution
AN - SCOPUS:84860692078
SN - 9781612848006
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 5645
EP - 5652
BT - 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Y2 - 12 December 2011 through 15 December 2011
ER -