Stability analysis of static recurrent neural networks using delay-partitioning and projection

• Published in: Neural networks Vol. 22; no. 4; pp. 343 - 347
• Main Authors: Du, Baozhu, Lam, James
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.05.2009; Elsevier
• Subjects: Algorithms; Applied sciences; Artificial Intelligence; Computer science; control theory; systems; Computer Simulation; Connectionism. Neural networks; Delay system; Delay-partitioning; Exact sciences and technology; Forecasting; Linear matrix inequality (LMI); Linear Models; Mathematics; Neural Networks (Computer); Pattern Recognition, Automated; Software; Stability; Static recurrent neural networks; Time Factors; Static recurrent neural networks; Delay system; Stability; Linear matrix inequality (LMI); Delay-partitioning; Performance evaluation; Hopfield neural nets; Recurrent neural nets; Conservatism; Partition method; Theoretical study; Lyapunov method; Projection; Stability criterion; Neural network; Delay; Time invariance; Asymptotic stability; Linear matrix inequality; Time interval; Software; Delay time; Lyapunov function
• ISSN: 0893-6080; 1879-2782
• DOI: 10.1016/j.neunet.2009.03.005

This paper introduces an effective approach to studying the stability of recurrent neural networks with a time-invariant delay. By employing a new Lyapunov–Krasovskii functional form based on delay partitioning, novel delay-dependent stability criteria are established to guarantee the global asymptotic stability of static neural networks. These conditions are expressed in the framework of linear matrix inequalities, which can be verified easily by means of standard software. It is shown, by comparing with existing approaches, that the delay-partitioning projection approach can largely reduce the conservatism of the stability results. Finally, two examples are given to show the effectiveness of the theoretical results.