Delay‐dependent asymptotic stability of BAM neural networks with time delay

Abstract

PurposeThe purpose of this paper is to examine the criteria of uniqueness of the equilibrium point and the new stability criteria for stability of the equilibrium point. The new stability condition is dependent on the size of delays.Design/methodology/approachThe global asymptotic stability of a class of delayed bi‐directional associative memory (BAM) neural networks is studied. Some new sufficient conditions are presented for the unique equilibrium point and the global stability of BAM neural networks with time delays by constructing Lyapunov functions and using the linear matrix inequality. A numerical example is presented to illustrate the effectiveness of the theoretical results.FindingsBased on the mathematical method and matrixes inequality skill, some criteria are obtained which contain the unique equilibrium point and the global stability of BAM neural networks.Research limitations/implicationsThe paper proposes the new Lyapunov function and new skill to compose matrixes inequality.Practical implicationsA very useful method for BAM neural network to judge the uniqueness of the equilibrium point and stability.Originality/valueThe new mathematical model is proposed about the production process, and the new control method is used in the temperature system for a double layers welded pipe in welding process.