Conic S-Procedure And Constrained Dissipativity
  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. 
Alexander L. Fradkov