### On H-infinity control for dead-time systems

*
Gjerrit Meinsma and Hans Zwart
*

There is a mistake in published version of this
paper in Equation (24). This has been corrected in the report
version of this paper (where it has the same equation number). The report
can be downloaded below. (Thanks to Stefan Strubbe for noting
the mistake.)

**Abstract**

A mixed sensitivity H-infinity problem is solved for
dead-time systems. 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 a related finite dimensional Riccati
equation has a solution with a certain nonsingularity property.
In the case of zero time-delay the Riccati equation is the standard
Riccati equation and the nonsingularity condition is that the solution
be nonnegative definite. For non-zero time-delay the non-singularity
condition is more involved but it still allows to obtain controllers.
All sub-optimal controllers are parameterized and the
central controller is shown to consist of an interconnection of a rational
system with a finite memory system, both of which can be implemented.
Some H-infinity problems are rewritten as pure
rational H-infinity problems using a Smith predictor
parameterization of the controller.

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

**Postscript file (the first version, with some errors):**
dead_time.ps.gz
(29 pages, 188 Kb, 600 dpi, gzip compressed).

**Pdf file (updated, corrected, shortened):**
dead_time.pdf
(160 Kb, 600 dpi).

**Matlab macros.**
The Matlab macros that we used for the examples in the paper
(Download them by pressing the shift and left-button simultaneously):
At present these macros may be difficult to understand if you do not have the
paper. As it is now, mxhans.m, mxglover.m and mxtoker.m are three examples
which, hopefully make clear how the macros are to be used.

**BibTex entry **

@Article{MZ97a,
author = "G. Meinsma and H. Zwart",
title = "On {$\mathcal{H}_\infty$} control for dead-time systems",
journal = "IEEE Trans. Aut. Control",
year = "2000",
volume = "45",
number = "2",
pages = "272-285"
}

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