LMI Approach for Stationary Oscillation of Interval Neural Networks With Discrete and Distributed Time-Varying Delays Under Impulsive Perturbations

2010 ◽  
Vol 21 (10) ◽  
pp. 1555-1563 ◽  
Author(s):  
Xiaodi Li ◽  
Jianhua Shen
Keyword(s):  
Neural Networks ◽  
Time Varying ◽  
Lmi Approach ◽  
Stationary Oscillation ◽  
Interval Neural Networks ◽  
Impulsive Perturbations

DELAY-DEPENDENT GLOBAL ROBUST ASYMPTOTIC STABILITY ANALYSIS OF BAM NEURAL NETWORKS WITH TIME DELAY: AN LMI APPROACH

2007 ◽  
Vol 03 (01) ◽  
pp. 57-68 ◽  
Author(s):  
XU-YANG LOU ◽  
BAO-TONG CUI
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Linear Matrix ◽  
Time Varying ◽  
Bam Neural Networks ◽  
Lmi Approach ◽  
Global Robust Asymptotic Stability ◽  
Dependent Property ◽  
Delay Dependent ◽  
Robust Asymptotic Stability

The global robust asymptotic stability of bi-directional associative memory (BAM) neural networks with constant or time-varying delays is studied. An approach combining the Lyapunov-Krasovskii functional with the linear matrix inequality (LMI) is taken to study the problem. Some a criteria for the global robust asymptotic stability, which gives information on the delay-dependent property, are derived. Some illustrative examples are given to demonstrate the effectiveness of the obtained results.

scholarly journals Robust Almost Periodic Dynamics for Interval Neural Networks with Mixed Time-Varying Delays and Discontinuous Activation Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-13
Author(s):  
Huaiqin Wu ◽  
Sanbo Ding ◽  
Xueqing Guo ◽  
Lingling Wang ◽  
Luying Zhang
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Time Varying ◽  
Almost Periodic ◽  
Activation Functions ◽  
Robust Exponential Stability ◽  
Discontinuous Activation ◽  
Interval Neural Networks ◽  
Discontinuous Activation Functions ◽  
Global Robust Exponential Stability

The robust almost periodic dynamical behavior is investigated for interval neural networks with mixed time-varying delays and discontinuous activation functions. Firstly, based on the definition of the solution in the sense of Filippov for differential equations with discontinuous right-hand sides and the differential inclusions theory, the existence and asymptotically almost periodicity of the solution of interval network system are proved. Secondly, by constructing appropriate generalized Lyapunov functional and employing linear matrix inequality (LMI) techniques, a delay-dependent criterion is achieved to guarantee the existence, uniqueness, and global robust exponential stability of almost periodic solution in terms of LMIs. Moreover, as special cases, the obtained results can be used to check the global robust exponential stability of a unique periodic solution/equilibrium for discontinuous interval neural networks with mixed time-varying delays and periodic/constant external inputs. Finally, an illustrative example is given to demonstrate the validity of the theoretical results.

scholarly journals Global Asymptotical Stability Analysis for Fractional Neural Networks with Time-Varying Delays

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 138
Author(s):  
Zhixin Zhang ◽  
Yufeng Zhang ◽  
Jia-Bao Liu ◽  
Jiang Wei
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Asymptotical Stability ◽  
Time Varying ◽  
Global Asymptotical Stability ◽  
Stability Criteria ◽  
Lmi Approach ◽  
Time Varying Delay ◽  
The Stability ◽  
Varying Delay

In this paper, the global asymptotical stability of Riemann-Liouville fractional-order neural networks with time-varying delays is studied. By combining the Lyapunov functional function and LMI approach, some sufficient criteria that guarantee the global asymptotical stability of such fractional-order neural networks with both discrete time-varying delay and distributed time-varying delay are derived. The stability criteria is suitable for application and easy to be verified by software. Lastly, some numerical examples are presented to check the validity of the obtained results.

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