Sensitivity analysis and computable bounds for the generalized algebraic Riccati equation

In this paper we study the effect of perturbations in the system matrices on the generalized Riccati equation. The topological aspects of the regular Riccati equation are generalized and the existence and uniqueness of a stabilizing solution to the generalized Riccati equation is guaranteed for sufficiently small perturbations in the system matrices. No assumptions are made about the stabilizability or detectability of the perturbed system. Further, bounds on the "sufficiently small" perturbations are provided which lead to computable bounds on the sensitivity of the solution.