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Stochastic Stability and H ∞ Disturbance Attenuation of A Class of Nonlinear Stochastic Delayed Systems
Author(s) -
Cao YongYan,
Hu Lisheng
Publication year - 2001
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 - 10.1111/j.1934-6093.2001.tb00067.x
Subject(s) - attenuation , disturbance (geology) , nonlinear system , mathematics , control theory (sociology) , stability (learning theory) , lyapunov function , computer science , physics , control (management) , paleontology , quantum mechanics , artificial intelligence , machine learning , optics , biology
In this paper, we consider stochastic stability analysis and H ∞ disturbance attenuation for a class of discrete‐time nonlinear stochastic retarded systems whose nonlinearities are described by statistical means. First a sufficient condition on mean square stability, which is independent of delay, is proposed using the stochastic Lyapunov functional approach. Then, H ∞ disturbance attenuation property of the system is analyzed. It is shown that the H ∞ disturbance attenuation of such nonlinear systems can be reduced to a linear matrix inequality problem.