  We consider matrix Riccati inequality arising in the theory of absolute
stability, $H_\infty$ control problem, $LQ$ problem, and optimal estimation
problem. In the case of sign definite frequency domain function, the
solvability of Riccati inequalities is a subject of the famous Kalman-
Yakubovich lemma. This paper presents necessary and sufficient conditions for
solvability of Riccati inequality in the general sign indefinite case. To this
end we use special representations of Hamiltonian matrices. The results are
illustrated by an example.
