Multivariable pi-sharing theory and its application on the Lur'e problem

The pi-sharing theory developed by Lawrence and Johnson (1986) is extended to handle square multivariable continuous-time systems, and for the most essential part of finding usable pi-coefficients, LMI formulations are utilized such that for any finite-dimensional LTI systems, time-invariant pi-coef...

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Bibliographic Details
Published in:IEEE transactions on automatic control 1998-10, Vol.43 (10), p.1501-1505, Article 1501
Main Authors: HU, S.-C, FONG, I.-K, KUO, T.-S
Format: Article
Language:English
Subjects:
Applied sciences
Computer science
control theory
systems
Control theory. Systems
Exact sciences and technology
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Linear matrix inequalities
MIMO
Nonlinear systems
Stability analysis
Symmetric matrices
System theory
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Summary:The pi-sharing theory developed by Lawrence and Johnson (1986) is extended to handle square multivariable continuous-time systems, and for the most essential part of finding usable pi-coefficients, LMI formulations are utilized such that for any finite-dimensional LTI systems, time-invariant pi-coefficients can be obtained easily. Furthermore, pi-coefficients are derived for sector-bounded nonlinearities, and the extended pi-sharing theory is applied to the multivariable Lur'e problem. With this approach, not only can a Lur'e system with known sector bounds on nonlinearities be checked for stability, but also the maximal bounds ensuring stability can be found under some conditions.
ISSN:0018-9286
1558-2523
DOI:10.1109/9.720518