A New Method for Stability Analysis of Recurrent Neural Networks With Interval Time-Varying Delay

• Published in: IEEE transactions on neural networks Vol. 21; no. 2; pp. 339 - 344
• Main Authors: Zuo, Zhiqiang, Yang, Cuili, Wang, Yijing
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.02.2010; Institute of Electrical and Electronics Engineers
• Subjects: Algorithms; Applied sciences; Artificial intelligence; Automatic control; Computer science; control theory; systems; Computer Simulation; Connectionism. Neural networks; Criteria; Decoupling; Delay; Delay effects; delay-range-dependent; Derivatives; Electric variables measurement; Exact sciences and technology; interval time-varying delay; Laboratories; Linear matrix inequalities; Lyapunov functions; Neural networks; Neural Networks (Computer); Process control; Recurrent neural networks; recurrent neural networks (RNNs); Stability analysis; stability criteria; Time Factors; Uncertainty; Recurrent neural nets; recurrent neural networks (RNNs); Lyapunov method; stability criteria; Neural network; Matrix function; Delay; Time varying system; Upper bound; Decoupling; Derivative; interval time-varying delay; Time interval; Delay time; Lyapunov function; delay-range-dependent
• ISSN: 1045-9227; 1941-0093
• DOI: 10.1109/TNN.2009.2037893

This brief deals with the problem of stability analysis for a class of recurrent neural networks (RNNs) with a time-varying delay in a range. Both delay-independent and delay-dependent conditions are derived. For the former, an augmented Lyapunov functional is constructed and the derivative of the state is retained. Since the obtained criterion realizes the decoupling of the Lyapunov function matrix and the coefficient matrix of the neural networks, it can be easily extended to handle neural networks with polytopic uncertainties. For the latter, a new type of delay-range-dependent condition is proposed using the free-weighting matrix technique to obtain a tighter upper bound on the derivative of the Lyapunov-Krasovskii functional. Two examples are given to illustrate the effectiveness and the reduced conservatism of the proposed results.