Brief paper: Linear matrix inequality tests for frequency domain inequalities with affine multipliers

Authors:
Matthew R. Graham;Mauricio C. de Oliveira
Affiliations:
University of California, San Diego, Department of Mechanical and Aerospace Engineering, 9500 Gilman Drive, La Jolla, CA 92093-0411, USA;University of California, San Diego, Department of Mechanical and Aerospace Engineering, 9500 Gilman Drive, La Jolla, CA 92093-0411, USA
Venue:
Automatica (Journal of IFAC)
Year:
2010

Citing 4
Cited 0

On the Kalman-Yakubovich-Popov lemma

Systems & Control Letters
Discrete Transforms, Semidefinite Programming, and Sum-of-Squares Representations of Nonnegative Polynomials

SIAM Journal on Optimization
Kalman-Popov-Yakubovich lemma and the S-procedure: A historical essay

Automation and Remote Control
Brief paper: An alternative Kalman-Yakubovich-Popov lemma and some extensions

Automatica (Journal of IFAC)

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Abstract

This paper revisits an alternative formulation of the Kalman-Yakubovich-Popov (KYP) Lemma, relating an infinite dimensional Frequency Domain Inequality (FDI) to a pair of finite dimensional Linear Matrix Inequalities (LMI). It is shown that this alternative formulation allows a certain class of the coefficient matrix of the FDI to be frequency dependent without introducing conservatism. The construction provided in the present paper is helpful in other problems where system augmentation is commonly used, such as those involving rational or polynomial multipliers for stability and performance analysis.