Robust Stability Criterion for Discrete-Time Uncertain Markovian Jumping Neural Networks With Defective Statistics of Modes Transitions

Authors:
Ye Zhao;Lixian Zhang;Shen Shen;Huijun Gao
Affiliations:
Space Control & Inertial Technol. Res. Center, Harbin Inst. of Technol., Harbin, China;-;-;-
Venue:
IEEE Transactions on Neural Networks
Year:
2011

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Abstract

This brief is concerned with the robust stability problem for a class of discrete-time uncertain Markovian jumping neural networks with defective statistics of modes transitions. The parameter uncertainties are considered to be norm-bounded, and the stochastic perturbations are described in terms of Brownian motion. Defective statistics means that the transition probabilities of the multimode neural networks are not exactly known, as assumed usually. The scenario is more practical, and such defective transition probabilities comprise three types: known, uncertain, and unknown. By invoking the property of the transition probability matrix and the convexity of uncertain domains, a sufficient stability criterion for the underlying system is derived. Furthermore, a monotonicity is observed concerning the maximum value of a given scalar, which bounds the stochastic perturbation that the system can tolerate as the level of the defectiveness varies. Numerical examples are given to verify the effectiveness of the developed results.