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On exponential stability conditions of linear neutral stochastic differential systems with time‐varying delay
Author(s) -
Cong S.
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.2818
Subject(s) - exponential stability , perturbation (astronomy) , stability (learning theory) , mathematics , regular polygon , control theory (sociology) , mean square , convex combination , lyapunov function , computation , exponential function , computer science , convex optimization , nonlinear system , control (management) , mathematical analysis , algorithm , physics , geometry , quantum mechanics , machine learning , artificial intelligence
SUMMARY We consider a class of neutral stochastic systems with time‐varying delay and study the exponential stability in the mean square sense. We derive sufficient stability conditions via applying Lyapunov functional method along with some practical techniques. Firstly, in computing the constructed Lyapunov functional, we make use of some basic rules of Itô calculus to reduce the conservatism produced by noise because it, in principle, plays a negative role for preserving stability in the mean square sense. Also, it is an important observation that, using some slack matrices, we can create convex conditions to accommodate the computation to time‐varying delay. In the sequel, we use a perturbation approach to estimate the decay rate of state and come to the conclusion of stability. Finally, we include an example to demonstrate the effectiveness of the method. Copyright © 2012 John Wiley & Sons, Ltd.