The Sensitivity of the Algebraic and Differential Riccati Equations

In this paper it is shown that the ideas developed by Byers in [Proc. Summer Research Conference, AMS Vol. 47, Contemporary Math., American Mathematical Society, Providence, RI, 1984, pp. 35–49] on the sensitivity of the algebraic Riccati equation can be sharpened and extended to norms other than the Frobenius norm. This extension is crucial from an interpretive point of view because use of the spectral norm allows an identification between the condition number of the algebraic Riccati equation and the damping properties of the closed-loop dynamical system. Moreover, this approach has the pleasant feature that it carries over to a completely parallel theory for the sensitivity of the differential Riccati equation, an area that has not been considered previously.