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Less Conservative Stability Criteria for Discrete‐Time Nonlinear Stochastic Singular Systems with Mixed Time‐Delay
Author(s) -
Weng Falu,
Ding Yuanchun,
Yang Guoliang,
Liang Liming,
Yu Zhongan
Publication year - 2013
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.709
Subject(s) - control theory (sociology) , linear matrix inequality , nonlinear system , mathematics , stability (learning theory) , discrete time and continuous time , controller (irrigation) , causality (physics) , computer science , control (management) , mathematical optimization , statistics , physics , quantum mechanics , artificial intelligence , machine learning , agronomy , biology
The problem of delay‐dependent robust stability and stabilization for discrete‐time nonlinear stochastic singular systems with mixed time delay is discussed in this paper. Based on a delay partitioning technique, a new description of the system is obtained first. Then, considering each subinterval, a novel delay‐dependent Lyapunov functional is established. In terms of the linear matrix inequality ( LMI ) technique, the delay‐dependent conditions are proposed for the system to be regular, causal, and mean‐square stable. Moreover, a suitable robust state feedback controller is designed, and the regularity, causality and stability of the closed‐loop system are guaranteed. Finally, numerical examples are given to show the results derived from the proposed method are less conservative than the existing ones.