The Stability Analysis And Stabilization For Time-Delay Neural Networks

Neural networks have received considerable attention due to their extensive applications in various signal processing problems such as optimization, fixed-point computations, and other areas in the past decades. It is well known that the phenomenon with time-delay can be found in the neural networks, and often results in not only lowering down the speed of the transmission but also the instability and oscillation. Therefore, more practical values can be received from the research into the asymptotic stability characters of the time-delay neural networks systems.By using the Lyapunov second method, linear matrix inequalities and matrices analysis, this paper studies the stability and the state feedback control of the time-delay neural networks systems. The main works is illustrated as follows:Firstly, the background of the research on stability and stabilization of the time-delay neural networks systems is introduced. In the first chapter, some basic notions are introduced, which are mainly categorized into fiver parts:(1) Conception of LMI; (2) LMI Toolbox; (3) Conception of S-procedure; (4) Relative lemmas and theory; (5) Explanation of Nomenclature. In the second chapter, the stability problems of the time-delay neural networks systems are studied. By using the Lyapunov second method, we give a system stability criterion in terms of linear matrix inequalities (LMIs). An illustrative example is given to display that the delay-dependent stability condition given by this paper is less conservative and easier to apply than the former results. In the third chapter, the stability problems of uncertain time-delay neural networks systems are considered. We provide a delay-dependent stability criterion, which is in terms of linear matrix inequalities (LMIs). Linear matrix inequalities can be conveniently solved by the toolbox in MATLAB. In the fourth and the fifth chapter, we study the stability problems of the distributed and the neutral time-delay neural networks, respectively. In the sixth chapter, the stabilization problems of neural networks systems are researched and the state feedback controller is designed. The simulation results are shown that the conclusion given is effective and easy to apply. At last, we sum up all the paper and give prospects of the stability and stabilization of the time-delay neural networks systems studies.