On impulsive modes of linear singular systems subject to decentralized output feedback

Some algebraic properties of linear singular systems at infinity under static decentralized output feedback are studied in this note. New concepts of algebraic multiplicity and geometric multiplicity of the impulsive decentralized fixed modes, and the impulsive decentralized cycle index of the singu...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2003-10, Vol.48 (10), p.1804-1809
Main Authors: Yu, Runyi, Wang, Dianhui
Format: Article
Language:English
Subjects:
Algebra
Applied sciences
Automatic control
Channels
Computer science
control theory
systems
Control system synthesis
Control systems
Control theory. Systems
Controllability
Decentralized
Differential equations
Exact sciences and technology
Infinity
Mathematical analysis
Matrices
Miscellaneous
Nonlinear control systems
Nonlinear equations
Nonlinear systems
Output feedback
Robust control
Stability analysis
Sun
System theory
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Summary:Some algebraic properties of linear singular systems at infinity under static decentralized output feedback are studied in this note. New concepts of algebraic multiplicity and geometric multiplicity of the impulsive decentralized fixed modes, and the impulsive decentralized cycle index of the singular system are defined. These concepts indicate how much a singular system can be made close to being impulse-free by decentralized output feedback, and the results are shown to be generic. The geometric multiplicity and the impulsive decentralized cycle index are determined in terms of the system matrices explicitly. The number of impulsive modes that can be eliminated is given in terms of these indexes. The impulsive decentralized cycle index is shown to characterize generic properties on controllability and observability of the closed-loop system through an individual channel (or an external channel). Illustrative examples are provided.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2003.817933