Investigating duality on stability conditions

This paper is devoted to investigate the role played by duality in stability analysis of linear time-invariant systems. We seek for a dual statement of a recently developed method for generating stability conditions, which combines Lyapunov stability theory with Finsler's Lemma. This method, de...

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Bibliographic Details
Published in:Systems & control letters 2004-05, Vol.52 (1), p.1-6
Main Author: de Oliveira, Maurı́cio C.
Format: Article
Language:English
Subjects:
Applied sciences
Computer science
control theory
systems
Control theory. Systems
Duality
Exact sciences and technology
Linear matrix inequalities
Linear systems
Optimization
Stability
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Summary:This paper is devoted to investigate the role played by duality in stability analysis of linear time-invariant systems. We seek for a dual statement of a recently developed method for generating stability conditions, which combines Lyapunov stability theory with Finsler's Lemma. This method, developed in the time domain, is able to generate a set of (primal) equivalent stability tests involving extra multipliers. The resulting tests have very attractive properties. Stability is characterized via linear matrix inequalities and we use optimization theory to obtain the duals. The dual problems are given a frequency domain interpretation.
ISSN:0167-6911
1872-7956
DOI:10.1016/j.sysconle.2003.09.011