Method of forbidden regions in the dynamic system matrices root clustering problem

New criteria for root-clustering of the dynamic system matrices in multiply connected regions were presented. A concept of the forbidden region was introduced, and a generalization of the Lyapunov-Jury theorem onto the multiply connected regions was proposed. The necessary and sufficient conditions...

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Bibliographic Details
Published in:Automation and remote control 2014-08, Vol.75 (8), p.1393-1401
Main Authors: Melnikov, V. G., Dudarenko, N. A.
Format: Article
Language:English
Subjects:
CAE) and Design
Calculus of Variations and Optimal Control
Optimization
Computer-Aided Engineering (CAD
Control
Linear Systems
Mathematics
Mathematics and Statistics
Mechanical Engineering
Mechatronics
Robotics
Systems Theory
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Summary:New criteria for root-clustering of the dynamic system matrices in multiply connected regions were presented. A concept of the forbidden region was introduced, and a generalization of the Lyapunov-Jury theorem onto the multiply connected regions was proposed. The necessary and sufficient conditions for root-clustering outside the forbidden region were established as a sequence of matrix inequalities. Construction of the conditions for root-clustering outside the frequency bands and robust root-clustering in multiply connected region was illustrated by way of examples.
ISSN:0005-1179
1608-3032
DOI:10.1134/S0005117914080049