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Event‐triggered control via impulses for exponential stabilization of discrete‐time delayed systems and networks
Author(s) -
Liu Bin,
Hill David J.,
Sun Zhijie,
Huang Jinxia
Publication year - 2019
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.4450
Subject(s) - control theory (sociology) , robustness (evolution) , computer science , discrete time and continuous time , exponential function , control (management) , exponential growth , mathematical optimization , mathematics , statistics , artificial intelligence , mathematical analysis , biochemistry , chemistry , gene
Summary This paper investigates the stabilization issue via event‐triggered controls (ETCs) for discrete‐time delayed systems (DDSs) and networks. Based on the recently proposed ETC scheme for discrete‐time systems without time delays, improved ETC (I‐ETC) and event‐triggered impulsive control (ETIC) are proposed for DDS. The algorithms for ETC, I‐ETC, and ETIC are given respectively to derive criteria of exponential stabilization of DDS. Moreover, the exponential stabilization and stabilization to ISS for discrete‐time delayed networks is achieved by employing the algorithms of ETC and ETIC. The issue of stabilization via ETCs for dynamical networks where different subsystems have different sequences of event instants is solved by introducing the check‐period into ETCs and establishing general ISS estimate of discrete‐time delayed inequality. In order to assess the performances of the control schemes, discussions on nontriviality are given by proposing the concept of rate of control and the function of control cost. Finally, two examples with numerical simulations are presented to demonstrate the effectiveness of theoretical results. From the obtained results on stabilization and the simulations, the ETIC is shown to have clear advantages and well performances than the classical state feedback control, the ETC recently proposed, I‐ETC, and the time‐based impulsive control on aspects of nontriviality, lower rate of control, lower cost of control, and robustness w.r.t. external disturbances.