=ADD=
=reftype=
14
=number=
97-37
=url=
ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1997/97-37.ps.gz
=note=
PhD Thesis
=sponsor=
ACCLAIM project sponsored by the European Community Basic Research Action
(ESPRIT 7195) and the Austrian Science Foundation (FWF Project No. P9374-PHY);
CEI PACT project sponsored by the Austrian Ministry of Science and Research.
=year=
1997
=author=
Neubacher; Andreas
=title=
Parametric Robust Stability by Quantifier Elimination
=month=
11
=abstract=
Stability analysis is a central aspect of the theory of differential
equations, especially for parameterized problems; one application area
where parametric stability plays an important rôle is control theory.  The
main goals of this thesis are to apply a quantifier elimination framework
consistently to various stability problems and to develop specialized
methods that solve these problems either symbolically or numerically with
mathematically guaranteed exactness more efficiently than general
quantifier elimination methods.

As a first step, known parametric robust stability problems and known
methods for solving parameter-free problems are formulated in a general
quantifier elimination framework.  This approach extends work done by other
authors on applying quantifier elimination theory to robust control and
parametric design problems.

A known stability test based on positiveness of the Hurwitz determinant is
generalized and new proofs are given for this test as well as for
Kharitonov's theorem.

In the case where parameters appear linearly and independently, a new
method for exactly computing the stability margin is presented.

In the case where parameters appear nonlinearly and depedently, new methods
for computing a lower bound on the stability margin and for exactly
computing the stability margin are developed.

Finally, a framework and a general method for approximate quantifier
elimination are presented.
=location=
2
=owner=
2
=source=
3