Newton's method for a rational matrix equation occurring in stochastic control

We study a general class of rational matrix equations, which contains the c ontinuous (CARE) and discrete (DARE) algebraic Riccati equations as special cases. Equations of this type were encountered in [SLAM J. Control and Opt imization 36 (1998) 1501-1538; Stochastics and Stochastics Reports, 65 (199 9) 255-297], where H-infinity-type problems of disturbance attenuation for stochastic linear systems were studied. We develop a unifying framework for the analysis of these equations based on the theory of (resolvent) positiv e operators and show that they can be solved by Newton's method starting at an arbitrary stabilizing matrix. (C) 2001 Elsevier Science Inc. All rights reserved.