Robust stability criterion for discrete-time uncertain Markovian jumping neural networks with defective statistics of modes transitions.
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.
Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin 150080, China. zhaoye8810@gmail.com
Ye
Y
Zhao
Lixian
L
Zhang
Shen
S
Shen
Huijun
H
Gao
D000465:Algorithms; D001185:Artificial Intelligence; D003198:Computer Simulation / Q000592:standards / Q000706:statistics & numerical data; D008390:Markov Chains; D016571:Neural Networks, Computer; D011336:Probability; D011340:Problem Solving; D012985:Software Design; D013269:Stochastic Processes; D013997:Time Factors