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In this paper we present an overview/tutorial of the existing results and a constructive solution for the suboptimal Hankel norm approximation problem for the Wiener class of infinite-dimensional systems. The presented approach is based on frequency domain techniques. The construction of a solution uses a recent result on the continuity of the J-spectral factorization in the Wiener norm. The Wiener...
Finite-dimensional approximations of partial differential equations are used not only for simulation, but also for controller design. Modal truncation and numerical approximation are common practical methods for approximating distributed parameter systems. The modal approximation preserves the exact, low-order poles of the original system. However, the zeros of modal approximations may differ significantly...
In this paper we approach the problem of moment matching for a class of infinite-dimensional systems, based on the unique solution of an operator Sylvester equation. It results in a class of parameterized, finite-dimensional, reduced order models that match a set of prescribed moments of the given system. We show that, by properly choosing the free parameters, additional constraints are met, e.g.,...
We compare the LQR control for a long-but-finite string of 2 × 2 MIMO systems with the LQR control for the corresponding infinite-dimensional spatially invariant system. We provide analytical and numerical examples where these are different and we investigate the cause. We also provide sufficient conditions for the LQR solutions to be similar as the length of the string increases. This work extends...
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