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Insensitive output feedback H ∞ control of delta operator systems with insensitivity to sampling time jitter
Author(s) -
Guo XiangGui,
Yang GuangHong
Publication year - 2012
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.2915
Subject(s) - delta operator , jitter , control theory (sociology) , lemma (botany) , transfer function , sampling (signal processing) , bounded function , sensitivity (control systems) , operator (biology) , domain (mathematical analysis) , time domain , computer science , mathematics , shift operator , control (management) , engineering , electronic engineering , mathematical analysis , filter (signal processing) , repressor , artificial intelligence , compact operator , ecology , chemistry , biology , telecommunications , biochemistry , transcription factor , computer vision , programming language , poaceae , electrical engineering , extension (predicate logic) , gene
SUMMARY The insensitive multi‐objective H ∞ control synthesis problem via dynamic output feedback for linear delta operator systems with insensitivity to sampling time jitter is investigated in the case of small sampling times. The delta‐domain model instead of the standard shift‐domain model is used to avoid the inherent numerical ill‐condition resulting from using the latter model at high sampling rates. Parameter sensitivity function of the transfer function with respect to sampling time is defined to mitigate the effect of sampling time jitter because it may cause significant degradation of the overall system performance. It is worth pointing out that a novel bounded real lemma for delta operator allowing extra degree of freedom for multi‐objective control design is presented by using the well‐known projection lemma. Then, from this new lemma, a two‐step design procedure based on LMI is presented to design insensitive dynamic output feedback controllers such that the resulting closed‐loop system is asymptotically stable and meets the requirement of sensitivity specification. A numerical example is also presented to show the effectiveness of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.