ON DAMPED ALGEBRAIC RICCATI-EQUATIONS

In a recent paper, an algorithm was proposed which produces dampening controllers based on damped algebraic Riccati equations (DARE's) deriv ed from a periodic Hamiltonian system. The solution to one of these DA RE's is symmetric and the other, skew-symmetric; both of these solutio ns 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 th e imaginary parts. In this paper, the authors extend these results to include a broader class: of damped algebraic Riccati equations which h ave Hermitian and skew-Hermitian solutions and show that every convex combination of these solutions produces a dampening feedback. This pro perty can be used to vary the feedback with two parameters and thus ob tain more flexibility in the controller design process.