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Improved stability conditions for discrete‐time systems under dynamic network protocols
Author(s) -
Liu Kun,
Seuret Alexandre,
Fridman Emilia,
Xia Yuanqing
Publication year - 2018
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.4247
Subject(s) - discrete time and continuous time , computer science , control theory (sociology) , scheduling (production processes) , stability (learning theory) , mathematical optimization , distributed computing , real time computing , mathematics , statistics , control (management) , artificial intelligence , machine learning
Summary This paper deals with the stability of discrete‐time networked systems with multiple sensor nodes under dynamic scheduling protocols. Access to the communication medium is orchestrated by a weighted try‐once‐discard or by an independent and identically‐distributed stochastic protocol that determines which sensor node can access the network at each sampling instant and transmit its corresponding data. Through a time‐delay approach, a unified discrete‐time hybrid system with time‐varying delays in the dynamics and in the reset conditions is formulated under both scheduling protocols. Then, a new stability criterion for discrete‐time systems with time‐varying delays is proposed by the discrete counterpart of the second‐order Bessel‐Legendre integral inequality. The developed approach is applied to guarantee the stability of the resulting discrete‐time hybrid system model with respect to the full state under try‐once‐discard or independent and identically‐distributed scheduling protocol. The communication delays can be larger than the sampling intervals. Finally, the efficiency of the presented approach is illustrated by a cart‐pendulum system.