From generalized KYP lemma to engineering applications

This paper proposes a generalized version of the Kalman-Yakubovic-Popov (KYP) lemma that establishes the equivalence between a frequency domain inequality (FDI) and a linear matrix inequality (LMI). Our new result allows us to treat (semi)finite frequency ranges and possibly nonproper transfer functions. We study implications of this generalization, and develop an interface between the basic result and various engineering applications. Specifically, it is shown that our result allows us to solve a certain class of system design problems with multiple specifications on the gain/phase properties in several frequency ranges.