### Unstable and nonproper weights in H-infinity control

*Gjerrit Meinsma
*

**Abstract**

In this note an ${\cal H}_\infty$ control problem is examined
where the controller can and need only stabilize a part of the
generalized closed loop due to unstable weights.
The procedure is a
trivial extension of known results and is computationally the easiest
method available.

**Keywords:**
${\cal H}_\infty$ control theory, stable fractions,
Riccati equations.

**Postscript file:**
unstable.ps.gz
(6 pages, 50 Kb, gzip compressed).

**BibTex entry**

@Article{GjMe95d,
author = {G. Meinsma},
title = {Unstable and nonproper weights in
$\mathcal{H}_\infty$ control},
journal = {Automatica},
year = {1995},
volume = {31},
number = {11},
pages = {1655--1658}
}

**More info**

In conjunction with this paper I wrote some Matlab macros
that can be used to solve the mixed sensitivity problem also if the shaping
filters are unstable or nonproper. The macros are availabe in two
flavors. The newest set is supposed to work for Matlab 5.3 with
the new toolboxes (mu-tools and the control toolbox):
The *newtest* explains how things work.
If you have **old** Matlab (version 4.x) or old versions of
mu-tools or control toolbox, use instead:
Here *mxtest* explains how things work.
The macros assume that the mu-toolbox is installed. Actually, of the
mu-toolbox only the macro **ric_schr.m** is used which computes the
stable eigenspace of a Hamiltonian matrix.

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