Stability Criteria for Recurrent Neural Networks With Time-Varying Delay Based on Secondary Delay Partitioning Method

• Published in: IEEE transaction on neural networks and learning systems Vol. 26; no. 10; pp. 2589 - 2595
• Main Authors: Wang, Zhanshan, Liu, Lei, Shan, Qi-He, Zhang, Huaguang
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.10.2015; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Computer Simulation; Criteria; Delay; Delay effects; Delays; Extended reciprocal convex combination (RCC); Humans; Integrals; Learning systems; Linear matrix inequalities; Mathematical models; Models, Theoretical; Neural networks; Neural Networks (Computer); Nonlinear Dynamics; Numerical stability; Partitioning; Recurrent neural networks; recurrent neural networks (RNNs); Stability; Stability criteria; Time Factors; time-varying delay; Upper bound; time-varying delay; recurrent neural networks (RNNs); Extended reciprocal convex combination (RCC); stability
• ISSN: 2162-237X; 2162-2388; 2162-2388
• DOI: 10.1109/TNNLS.2014.2387434

A secondary delay partitioning method is proposed to study the stability problem for a class of recurrent neural networks (RNNs) with time-varying delay. The total interval of the time-varying delay is first divided into two parts, and then each part is further divided into several subintervals. To deal with the state variables associated with these subintervals, an extended reciprocal convex combination approach and a double integral term with variable upper and lower limits of integral as a Lyapunov functional are proposed, which help to obtain the stability criterion. The main feature of the proposed result is more effective for the RNNs with fast time-varying delay. A numerical example is used to show the effectiveness of the proposed stability result.