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Krylov-based model order reduction of time-delay systems. (English) Zbl 1247.65086
The main purpose of the paper is to reduce a time delay system with a single input and a single output to a delay-free model of a given dimension. The authors initially rewrite the system in a linear infinite dimensional form. The new system is discretized yielding an approximation that involves large matrices and no delays. The discretized system except of the approximating properties of the spectrum also fulfills a moment matching property, i.e., several derivatives at the origin and the first derivative at infinity of the original transfer function and its corresponding approximation coincide. Since the dimension of the state space on the discretized model is much larger than the state space dimension of the original time-delay system, a dynamic Arnoldi method for infinite dimensional systems is used to reduce its dimension. The preservation of moments is guaranteed. The whole method is illustrated by a numerical example given at the end of the paper.

MSC:
65K10 Numerical optimization and variational techniques
93A15 Large-scale systems
93B11 System structure simplification
93C15 Control/observation systems governed by ordinary differential equations
93D25 Input-output approaches in control theory
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