Generalized KYP Lemma With Real Data

A recent generalization of the Kalman-Yakubovich-Popov (KYP) lemma establishes the equivalence between a semi-infinite inequality on a segment of a line or circle in the complex plane and a linear matrix inequality (LMI). In this technical note we show that when the data are real, the matrix variables in the LMI can be restricted to be real, even when the frequency range is asymmetric with respect to the real axis.

[1]  Goele Pipeleers,et al.  Generalised repetitive control: relaxing the period-delay-based structure , 2009 .

[2]  Guang-Hong Yang,et al.  A finite frequency approach to filter design for uncertain discrete‐time systems , 2008 .

[3]  Siep Weiland,et al.  Damping Oscillations in Electrical Power Systems: a Dissipativity Approach , 2007, 2007 IEEE International Conference on Control Applications.

[4]  Shinji Hara,et al.  Feedback control synthesis of multiple frequency domain specifications via generalized KYP lemma , 2007 .

[5]  Lihua Xie,et al.  A generalized KYP lemma based control design and application for 425 kTPI servo track writing , 2006, 2006 American Control Conference.

[6]  Carsten W. Scherer,et al.  LMI Relaxations in Robust Control , 2006, Eur. J. Control.

[7]  Shinji Hara,et al.  Generalized KYP lemma: unified frequency domain inequalities with design applications , 2005, IEEE Transactions on Automatic Control.

[8]  Venkataramanan Balakrishnan,et al.  Semidefinite programming duality and linear time-invariant systems , 2003, IEEE Trans. Autom. Control..

[9]  T. Başar.  Absolute Stability of Nonlinear Systems of Automatic Control , 2001 .

[10]  T. Iwasaki,et al.  Generalized S-procedure and finite frequency KYP lemma , 2000 .

[11]  A. Rantzer.  On the Kalman-Yakubovich-Popov lemma , 1996 .

[12]  Adi Ben-Israel,et al.  More on linear inequalities with applications to matrix theory , 1971 .

[13]  R. Kálmán.  LYAPUNOV FUNCTIONS FOR THE PROBLEM OF LUR'E IN AUTOMATIC CONTROL. , 1963, Proceedings of the National Academy of Sciences of the United States of America.