Relaxing the detectability condition for the algebraic Riccati equation
Fangyuan Tan, William G. Vogt, M.H. Mickle · Electronics Letters · 1987
For a linear system, the detectability condition can be weakened to the Hamiltonian matrix composed of (A, B, Q, R) having eigenvalues with nonzero real parts, for the existence of the unique positive semidefinite stabilising solution of the algebraic Riccati equation. This condition yields the optimal feedback gain and can always be easily obtained by a given iterative technique.