We present the input-normal Riccati parameterization, a generalization
of Kabamba's input-normal form [1], which allows the continuous param
eterization of the set of minimal linear systems of a given order that
have distinct singular values; the input-normal Riccati form has no r
equirement that the underlying system be stable. We also present formu
las for the use of the input-normal Riccati parameterization for the s
ynthesis of systems via gradient methods.