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Robust exponential l 2 − l ∞ control for discrete‐time switched system: A cone complement linearization method
Author(s) -
Hou Linlin,
Zong Guangdeng,
Wu Yuqiang
Publication year - 2011
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.1013
Subject(s) - control theory (sociology) , exponential stability , mathematics , controller (irrigation) , complement (music) , dwell time , exponential function , norm (philosophy) , linearization , discrete time and continuous time , bounded function , computer science , mathematical analysis , control (management) , nonlinear system , law , physics , artificial intelligence , chemistry , biology , biochemistry , quantum mechanics , political science , agronomy , medicine , clinical psychology , statistics , complementation , gene , phenotype
SUMMARY The robust exponential l 2 − l ∞ control problem is considered in this paper for discrete‐time switched systems with both time‐varying delay and norm‐bounded parameter uncertainties. An exponential l 2 − l ∞ performance index is first introduced for the discrete‐time switched systems. The designed controller is a memory exponential l 2 − l ∞ controller. By introducing an average dwell time approach and a Lyapunov–Krasovskii functional technique, some sufficient criteria guaranteeing exponential stability are presented, and the desired memory exponential l 2 − l ∞ controller is established by resorting to a cone complement linearization method. Some results on exponential stability using memoryless exponential l 2 − l ∞ controller and asymptotical stability with traditional l 2 − l ∞ performance index are also established. Finally, a numerical example is provided to demonstrate that the proposed approach can lead to less conservatism compared with the developed result using memoryless exponential l 2 − l ∞ controller and asymptotical stability analysis with traditional l 2 − l ∞ performance index. Copyright © 2011 John Wiley & Sons, Ltd.