  A new version of classical S-procedure in system theory is proposed based on
duality in the space of positive definite matrices and introduction of matrix
Lagrange multipliers. A new proof and extension of the recent results of
T.Iwasaki, S. Hara, A. Fradkov ( Systems & Control Letters, 2005. Vol 54 (7),
pp 681-691) concerning equivalence between frequency domain inequality on
finite frequency range and constrained dissipativity property for linear
systems is given. The results of this paper extend S-procedure to allow for
analysis and design of systems with matrix inequalities constraints.
