INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, VOL. 1,229-294 (1991) zyx A FACTORIZATION PRINCIPLE FOR STABILIZATION OF LINEAR CONTROL SYSTEMS JOSEPH A. BALL zyxwv Department of Mathematics, Virginia Tech., Blacksburg, VA 24061. U.S.A. J. WILLIAM HELTON Department of Mathematics, University of California, San Diego, La Jolla, CA 92093, U.S.A zy . AND MADANPAL VERMA Department of Electrical Engineering, McGill University, Montreal, Quebec, Canada H3A 2KC SUMMARY By introducing a fictitious signal yo if necessary we define a transform of a given linear control system which generalizes the passage from the scattering to the chain formalism in circuit theory. Given a factorization zyxwvut b= zyxwv 0R of $where R is a block matrix function with a certain key block equal to a minimal phase (or outer) matrix function, we show that a given compensator zyxw U = Ky is internally stabilizing for the system B if and only if a related compensator K' is stabilizing for 0. Factorizations zy 9'= 0R with 0 having a certain block upper triangular form lead to an alternative derivation of the Youla parametrization of stabilizing compensators. Factorizations with 0 equal to a J-inner matrix function (in a precise weak sense) lead to a parametrization of all solutions K of the zyx H" problem associated with 9. This gives a new solution of the H" problem completely in the transfer function domain. Computation of the needed factorization B= 0R in terms of a state-space realization of 9' leads to the state-space formulas for the solution of the H" problem recently obtained in the literature. KEY WORDS Feedback stabilization H" control J-inner-outer factorization J-spectral factorization 0. INTRODUCTION A standard general feedback configuration in terms of which many problems of interest in This paper was recommendedfor publication by editor M. J. Grimble lO49-8923/9 l/O40229-66$33 .OO 0 1991 by John Wiley & Sons, Ltd. Received 7 July 1991 Revised September 1991