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J. Symbolic Computation (1995) 11, 1--6 Application of Quantifier Elimination Theory to

Summary: J. Symbolic Computation (1995) 11, 1--6
Application of Quantifier Elimination Theory to
Robust Multi­objective Feedback Design
P. Dorato y , Wei Yang y , and C. Abdallah y
y Department of Electrical and Computer Engineering, University of New Mexico
Albuquerque, NM 87131­1356, USA
(Received 30 September 1995)
This paper shows how certain robust multi­objective feedback design problems can be
reduced to quantifier elimination (QE) problems. In particular it is shown how robust
stabilization and robust frequency domain performance specifications can be reduced
to systems of polynomial inequalities with suitable logic quantifiers, 8 and 9. Because
of computational complexity the size of problems that can solved by QE methods is
limited. However the design problems considered here do not have analytical solutions,
so that even the solution of modest sized problems may be of practical interest.
1. Introduction
In 1975 Anderson et al. (Anderson & Bose & Jury 1975) proposed the application
of Tarski­Seidenberg decision theory (Tarski 1951, Seidenberg 1954) for the solution of
the static output feedback stabilization problem. The static output feedback stabilization
problem is one of the most important open problems in feedback design. The problem
can be stated mathematically as follows: find a matrix K such that all of the eigenval­


Source: Abdallah, Chaouki T- Electrical and Computer Engineering Department, University of New Mexico


Collections: Engineering