Decay of Hankel singular values of analytic control systems

Reference:

Opmeer, M. R., 2010. Decay of Hankel singular values of analytic control systems. Systems & Control Letters, 59 (10), pp. 635-638.

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Official URL:

http://dx.doi.org/10.1016/j.sysconle.2010.07.009

Abstract

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.

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