Decay of Hankel singular values of analytic control systems

Mark R Opmeer

OAI: oai:purehost.bath.ac.uk:publications/334e80f3-3e45-42c6-8c93-59b9bc57965d • DOI: https://doi.org/10.1016/j.sysconle.2010.07.009

We show that control systems with an analytic semigroup and control and observation operators that are not too unbounded have a Hankel operator that belongs to the Schatten class S-p for all positive p. This implies that the Hankel singular values converge to zero faster than any polynomial rate. This in turn implies fast convergence of balanced truncations. As a corollary, decay rates for the eigenvalues of the controllability and observability Gramians are also provided. Applications to the heat equation and a plate equation are given.

Model order reduction Infinite-dimensional systems Hankel operator