Stability Analysis For Several Classes Of Neural Networks With Time-varying Delay

The stability of four classes of neural networks with time-varying delays are inves-tigated by using the matrix theory, linear matrix inequalities technique and Lyapunovstability method. Some improved delay-dependent stability criteria are derived in termsof linear matrix inequalities.The general development of neural networks is reviewed. Then, the background ofresearch and the status of current research on the stability of neural networks are intro-duced. And the main works of this paper are sketched.The problem of delay-dependent asymptotic stability criteria for neural networkswith time-varying delay is considered. Based on the Lyapunov functional method andmatrix inequality technique, a new class of Lyapunov functional which contains a triple-integral term is constructed to derive some new delay-dependent stability criteria in termsof linear matrix inequalities. Finally, two numerical examples are given to show the meritsof our derived method.The problem of exponential stability criteria for neural networks with discrete time-varying delay and distributed time-varying delay is considered. By dividing the discretedelay interval into multiple segments and choosing a new class of Lyapunov functionalwhich contains tripe-integral terms, some new delay dependent stability criteria are de-rived in terms of linear matrix inequalities. The obtained criteria are less conservativebecause free-weighting matrices method and a convex optimization approach are con-sidered. Finally, two numerical examples are given to show the merits of the proposedmethod.The problem of stability criteria of neural networks with two additive time-varyingdelay components is investigated. Some new delay-dependent stability criteria are derivedin terms of linear matrix inequalities by choosing a new class of Lyapunov functional.The obtained criteria are less conservative because reciprocally convex approach is con-sidered. Finally, a numerical example is given to show the merits of the proposed method.The problem of stochastic stability criterion of Markovian jumping neural networkswith mode-dependent time-varying delays and partially known transition rates is consid-ered. Some new delay-dependent stability criteria are derived by choosing a new class of Lyapunov functional. The obtained criteria are less conservative because free-weightingmatrices method and a convex optimization approach are considered. Finally, a numericalexample is given to show the merits of the proposed method.