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Finite‐time stabilization of Markovian jump delay systems – a switching control approach
Author(s) -
Wen Jiwei,
Nguang Sing Kiong,
Shi Peng,
Peng Li
Publication year - 2016
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.3575
Subject(s) - dwell time , control theory (sociology) , attenuation , robustness (evolution) , settling time , bounded function , jump , markov process , controller (irrigation) , interval (graph theory) , computer science , mathematics , control (management) , engineering , control engineering , physics , step response , artificial intelligence , mathematical analysis , chemistry , optics , biology , biochemistry , quantum mechanics , gene , agronomy , medicine , clinical psychology , statistics , combinatorics
Summary In this paper, a finite‐time stabilization problem is considered for a class of continuous‐time Markovian jump delay systems (MJDSs). A switching controller, which only depends on the average dwell time (ADT) switching laws, is proposed to make a trade‐off between robustness and adaptiveness when the design complexity of mode‐independent, mode‐dependent, and mode‐dependent and variation‐dependent control strategies is considered. First, the stochastic finite‐time boundedness for an MJDS is analyzed by an ADT approach. Second, the disturbance attenuation capability of MJDS is studied via a finite‐time weighted L 2 gain, which depends on the switching numbers. The impacts of finite‐time interval and L 2 gain acting on the ADT are also thoroughly discussed. Then, a switching controller is designed such that the resulting closed‐loop MJDS is stochastically finite‐time bounded and has a guaranteed disturbance attenuation level. Finally, a numerical example is provided to verify the effectiveness of the developed results. Copyright © 2016 John Wiley & Sons, Ltd.