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Two slow stabilizing switching laws for discrete time positive switched systems
Author(s) -
Zheng Yan,
Feng Gang
Publication year - 2013
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.3032
Subject(s) - control theory (sociology) , lyapunov function , law , quadratic equation , diagonal , observer (physics) , mathematics , state (computer science) , stability (learning theory) , computer science , control (management) , physics , nonlinear system , algorithm , artificial intelligence , political science , geometry , quantum mechanics , machine learning
SUMMARY On the basis of a linear copositive Lyapunov function (LF) and a diagonal quadratic LF, respectively, two slow stabilizing switching laws are proposed for discrete time positive switched systems composed of m ( m ⩾ 2 ) subsystems. Under these two stabilizing switching laws, the LFs are allowed to increase in state‐driven intervals while the stability of positive switched systems is maintained. In addition, it is shown that positive switched systems under these two slow switching laws are robust against certain classes of perturbations. Furthermore, when the states of the systems are not available, observer‐based stabilizing switching laws for positive switched systems are also proposed. Some numerical examples are finally given to illustrate the effectiveness of the proposed stabilizing switching laws. Copyright © 2013 John Wiley & Sons, Ltd.