On integral input-to-state stability for a feedback interconnection of parameterised discrete-time systems

This paper addresses integral input-to-state stability (iISS) for a feedback interconnection of parameterised discrete-time systems involving two subsystems. Particularly, we give a construction for a smooth iISS Lyapunov function for the whole system from the sum of nonlinearly weighted Lyapunov fu...

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Bibliographic Details
Published in:International journal of systems science 2016-05, Vol.47 (7), p.1598-1614
Main Authors: Noroozi, N., Khayatian, A., Ahmadizadeh, S., Karimi, H.R.
Format: Article
Language:English
Subjects:
0-global asymptotic stability
Cascades
Construction
Feedback
input-to-state stability
integral input-to-state stability
Integrals
Interconnection
Lyapunov functions
parameterised discrete-time systems
small-gain conditions
Stability
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Summary:This paper addresses integral input-to-state stability (iISS) for a feedback interconnection of parameterised discrete-time systems involving two subsystems. Particularly, we give a construction for a smooth iISS Lyapunov function for the whole system from the sum of nonlinearly weighted Lyapunov functions of individual subsystems. Motivations for such a construction are given. We consider two main cases. The first one investigates iISS for the whole system when both subsystems are iISS. The second one gives iISS for the interconnected system when one of subsystems is allowed to be input-to-state stable. The approach is also valid for both discrete-time cascades and a feedback interconnection of iISS and static systems. Examples are given to illustrate the effectiveness of the results.
ISSN:0020-7721
1464-5319
DOI:10.1080/00207721.2014.942242