### The standard H-infinity control problem for dead-time systems

*
Gjerrit Meinsma and Hans Zwart
*

**Abstract**

The standard H-infinity control problem is solved for systems with
a delay. It is shown that for a given bound on the
H-infinity norm there exist causal stabilizing controllers that
achieve this bound if and only if two *rational* spectral
factorization problems have solutions with a certain nonsingularity
property. All sub-optimal controllers are parameterized and the
central controller is shown to consist of an interconnection of a
finite dimensional system with a system whose impulse response has
compact support.
*This note was submitted to the MTNS 1998. For the time being you can
download it here. The older version of this note contains a mistake
(a matrix was missing). This has been corrected in the present version
*

**Keywords:**
Dead-time systems, delay systems, H-infinity control,
Smith predictors, infinite dimensional systems.

**Postscript file:**
mtns98.ps.gz
(5 pages, 145 Kb, 600 dpi, gzip compressed).

**BibTex entry**

@InProceedings{MZb,
author = "G. Meinsma and H. Zwart",
title = "The standard {$\mathcal{H}_\infty$} control
problem for dead-time systems",
booktitle = "proceedings of the Mathematical Theory of Networks and
Systems '98",
pages = "317-320",
year = "1999"
}

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