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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