On the solvability of extended Riccati equations

The Kalman-Yakubovich-Popov lemma, which gives necessary and sufficient conditions for solvability of matrix LurʹeRiccati equations, is a milestone in modern control theory. There are, however, important and general extensions of this lemma that have not been studied yet. Starting with the absolute stability theory with semidefinite frequency domain function, we generalize here this lemma to the sign indefinite case-a research that is motivated by new problems on passivity and H/sub (infinity)/ control theory.