On damped algebraic Riccati equations

In a recent paper, an algorithm was proposed which produces dampening controllers based on damped algebraic Riccati equations (DAREs) derived from a periodic Hamiltonian system. The solution to one of these DAREs is symmetric and the other is skew-symmetric; both of these solutions lead to a dampening feedback, i.e., a stable closed-loop system for which the real parts of the eigenvalues are larger in modulus than the imaginary parts. In this paper, the authors extend these results to include a broader class of damped algebraic Riccati equations which have Hermitian and skew-Hermitian solutions and show that every convex combination of these solutions produces a dampening feedback. This property can be used to vary the feedback with two parameters and thus obtain more flexibility in the controller design process