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Asymptotic stability and stabilization for a class of nonlinear descriptor systems with delay
Author(s) -
Wu Jiancheng,
Wo Songlin,
Lu Guoping
Publication year - 2011
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.309
Subject(s) - exponential stability , uniqueness , control theory (sociology) , nonlinear system , parameterized complexity , mathematics , linear matrix inequality , bounded function , stability (learning theory) , norm (philosophy) , state (computer science) , full state feedback , class (philosophy) , computer science , mathematical optimization , control (management) , mathematical analysis , algorithm , artificial intelligence , law , physics , quantum mechanics , machine learning , political science
This paper discusses asymptotic stability and stabilization for a class of nonlinear descriptor systems with delay. The nonlinearity of the system is a continuous function of the time and system state, and the Jacobi matrix of the function is norm‐bounded. A sufficient condition for the existence and uniqueness of the solution to the descriptor system is proposed by a linear matrix inequality (LMI) approach. Under the condition, using nonlinear methods, the asymptotic stability for the system is obtained. In addition, to stabilize the descriptor system, a parameterized representation of the state feedback controller is given in terms of a solution to an LMI. Finally, the effectiveness of the approach is illustrated by numerical examples. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society