Title: The geometry of the generalized algebraic Riccati equation and of the singular Hamiltonian system,
Abstract: This paper analyzes the properties of the solutions of the generalized
continuous algebraic Riccati equation from a geometric perspective. This
analysis reveals the presence of a subspace that may provide an appropriate
degree of freedom to stabilize the system in the related optimal control
problem even in cases where the Riccati equation does not admit a stabilizing
solution.