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Robust stability of singularly perturbed descriptor systems with uncertain Markovian switchings and nonlinear perturbations
Author(s) -
Wang Guoliang,
Zhang Qingling,
Yang Chunyu
Publication year - 2012
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.2058
Subject(s) - mathematics , uniqueness , nonlinear system , scalar (mathematics) , control theory (sociology) , lyapunov function , stability (learning theory) , exponential stability , linear matrix inequality , mathematical optimization , mathematical analysis , computer science , control (management) , physics , geometry , quantum mechanics , artificial intelligence , machine learning
SUMMARY This paper is concerned with the problem of robust stability of Markovian jump singularly perturbed descriptor systems with uncertain switchings and nonlinear perturbations for any ε ∈ 0 , ε ̄, whereε ̄ is a pre‐defined positive scalar. A linear matrix inequality (LMI) condition is firstly established to guarantee the existence and uniqueness of a solution. Then, an ε ‐independent condition in terms of LMI related toε ̄ is derived via using an ε ‐dependent Lyapunov function, where the solution exists uniquely and is globally exponentially mean‐square stable simultaneously. Finally, numerical examples are used to show the feasibility and effectiveness of the given theoretical results. Copyright © 2012 John Wiley & Sons, Ltd.