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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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
Feedback
Linear matrix inequalities
MIMO
Nonlinear systems
Stability analysis
Symmetric matrices
System theory
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description 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.
doi_str_mv 10.1109/9.720518
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subjects Applied sciences
Computer science
control theory
systems
Control theory. Systems
Exact sciences and technology
Feedback
Linear matrix inequalities
MIMO
Nonlinear systems
Stability analysis
Symmetric matrices
System theory
title Multivariable pi-sharing theory and its application on the Lur'e problem
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