On a rational matrix equation occuring in stochastic control
Tobias Damm, D. Hinrichsen · 1999
We regard a general class of rational matrix equations, which contains the continuous (CARE) and discrete (DARE) algebraic Riccati equations as special cases. Equations of this type were encountered in [EIIPSG] and [EHP98] where H∞-typo. 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 (rcsolvcnt) positive operators and show that they can be solved by Newton's method starting at an arbitrary stabilizing matrix.