Input-to-State Stability for Nonlinear Systems With Large Delay Periods Based on Switching Techniques

The paper is concerned with the problem of input-to-state stability (ISS) for nonlinear delay systems with large delay periods (LDP). The concepts of the length rate of LDP and the frequency of LDP are introduced. First the considered system is converted into a switched delay system which may includ...

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Bibliographic Details
Published in:IEEE transactions on circuits and systems. I, Regular papers Regular papers, 2014-06, Vol.61 (6), p.1789-1800
Main Authors: Sun, Xi-Ming, Du, Sheng-Li, Shi, Peng, Wang, Wei, Wang, Li-Dong
Format: Article
Language:English
Subjects:
Delay
Delay systems
Delays
Dynamical systems
Inequalities
International Space Station
ISS
large delay periods
Nonlinear systems
Nonlinearity
Series (mathematics)
Stability
Stability criteria
Sun
switched delay systems
Switches
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Summary:The paper is concerned with the problem of input-to-state stability (ISS) for nonlinear delay systems with large delay periods (LDP). The concepts of the length rate of LDP and the frequency of LDP are introduced. First the considered system is converted into a switched delay system which may include an unstable subsystem. Then based on a piecewise Lyapunov functional, the ISS properties of the systems are developed under the constraints of the length rate and the frequency of LDP. ISS for a special kind of nonlinear delay systems is also considered and the conditions of nonlinear matrix inequalities (NLMIs) are proposed to guarantee the ISS properties of such a system. A numerical example and an example of a series DC motor are given to show the effectiveness of the proposed methods.
ISSN:1549-8328
1558-0806
DOI:10.1109/TCSI.2013.2295008