Title/Authors
Parameter dependent H infinity control by finite dimensional LMI
optimization: application to trade-off dependent control
M. Dinh,
G. Scorletti, V. Fromion and E. Magarotto
Abstract
In this paper, we consider the design of an H infinity trade-off
dependent controller, that is, a controller such that, for a given
Linear Time-Invariant plant, a set of performance trade-offs
parameterized by a scalar theta is satisfied. The controller
state space matrices are explicit functions of theta. This new problem
is a special case of the design of a parameter
dependent controller for a parameter dependent plant, which has many
application in Automatic Control.
This last design problem can be naturally formulated as a convex but
infinite dimensional optimization problem
involving parameter dependent Linear Matrix Inequality (LMI)
constraints. In this paper, we propose finite
dimensional (parameter independent) LMI constraints which are
equivalent to the parameter dependent
LMI constraints. The parameter dependent controller design is then
formulated as a convex finite dimensional
LMI optimization problem. The obtained result is then applied to the
trade-off dependent controller
design. A numerical example emphasizes the strong interest of our
finite dimensional optimization problem
with respect to the trade-off dependent control application.
Status
Accepted to IFAC World Congress on Automatic Control, July 2005.
Accepted to IJNRC, 2005.
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Bibtex reference
@ARTICLE{DSFM:05,
AUTHOR = "M.~Dinh and
G.~Scorletti and V.~Fromion and E.~Magarotto",
TITLE
= "Parameter dependent
{${H}_\infty$} control by finite dimensional {LMI} optimization:
application to trade-off dependent control",
JOURNAL = "Int.\ J.\ Robust
and Nonlinear Control",
YEAR
= "2005",
volume
= "15",
pages
= "383-406"}