Toward a Comprehensive Impossibility Result for String Stability

We provide a comprehensive impossibility result toward achieving string stability, i.e., keeping local relative errors in check with local controllers independently of the size of a chain of subsystems. We significantly extend the existing results, from the linear time-invariant (LTI) setting to any...

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Bibliographic Details
Published inIEEE transactions on automatic control Vol. 65; no. 4; pp. 1652 - 1659
Main Authors Farnam, Arash, Sarlette, Alain
Format Journal Article
LanguageEnglish
Published New York IEEE 01.04.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Communication
Control stability
Controllers
Couplings
Decentralized control
fault tolerant control
Linear systems
networked control systems
nonlinear control systems
Sensors
Stability criteria
Strain
Strings
Subsystems
traffic control
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Summary:We provide a comprehensive impossibility result toward achieving string stability, i.e., keeping local relative errors in check with local controllers independently of the size of a chain of subsystems. We significantly extend the existing results, from the linear time-invariant (LTI) setting to any homogeneous controllers that can be nonlinear, time varying, and locally communicating. We prove this impossibility for a set of definitions with various norm choices, including the <inline-formula><tex-math notation="LaTeX">L_2</tex-math></inline-formula>-type standard and a bounded-input implies bounded-output (BIBO) type criterion. All the results hold for a general discrete-time controller, which should cover most applications.
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content type line 14
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2019.2929967