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Numerical issues related to the computational solution of the algebraic matrix Riccati equation are discussed. The approach presented uses the generalized eigenproblem formulation for the solution of general forms of algebraic Riccati equations arising in both continuous- and discrete-time applications. These general forms result from control and filtering problems for systems in generalized (or implicit or descriptor) state space form. A Newtontype iterative refinement procedure for the generalized Riccati solution is given. The issue of numerical condition of the Riccati problem is addressed. Balancing to improve numerical condition is discussed. An overview of a software package, RICPACK, coded in portable, reliable Fortran is given. Results of numerical experiments are reported.
Arnold et al. (Sun,) studied this question.