Stability Analysis, Neural Networks With Delay

The delayed neural networks exhibits the rich and colorful dynamical behaviors,which are important parts of the delayed neural systems.Recently,many interesting stability criteria (such as asymptotic stability,exponential stability and absolute stability) for the equilibriums of delayed neural networks have been derived via Lyapunov functional approaches. Bidirectional associative memory(BAM) neural networks are autoassociations as well as heteroassociations. Due to the vast applications in pattern recognition,artificial intelligence, automatic control and other engineering fields,the stability issues of delayed BAM neural networks have attracted worldwide attention.A neural network is usually called an interval neural networks when the uncertainty is only due to the bounded deviations and perturbations of its parameters.The study on the stability of delayed interval neural networks becomes an important topic in theory and real applications.In this thesis,we consider the stability and state estimation problems for a class of delayed neural networks.The main results are as follows:1) Delay-dependent asymptotic stability criteria of BAM neural networks with timevarying delays.The problem of delay-dependent robust asymptotic stability for a class of BAM neural networks with time-varying delays is studied.Both differentiable and unnecessarily differentiable types of time-varying delays are involved.The activation functions are only assumed to be bounded.By introducing new integral inequality approach,several novel delay-dependent sufficient conditions are derived guaranteeing the asymptotic stability of given delayed BAM neural networks.All the conditions are expressed in terms of LMIs,which can be easily checked by resorting to the recently developed algorithms.Numerical examples are provided to illustrate the reduced conservatism of the proposed algorithms.It is shown that the stability results obtained in this thesis are effective and less conservative.2) Novel delay-dependent asymptotic stability conditions for BAM neural networks of neutral type.We deal with the problem of the delay-dependent asymptotic stability and robust asymptotic stability for delayed BAM neural networks of neutral type.Two cases of time delays in which whether the neutral delays are equal to the state delays or not are involved.By constructing a new Lyapunov-Krasovskii functional,employing Lyapunov-Krasovskii theoty and some new integral inequalities,several novel delay-dependent conditions are established checking the asymptotic stability for BAM neural networks and robust asymptotic stability for BAM neural networks of neutral type with uncertain parameters.The parameters uncertainties are expressed in a linear fractional form,which includes the norm bounded uncertainties as a special case.All the conditions are presented in terms of linear matrix inequalities(LMIs),which can be easily checked by utilizing the recently developed algorithms solving LMIs.Numerical examples are provided to illustrate the effectiveness of the proposed stability result.3) The state estimation design for BAM neural networks of neutral type.The state estimation problem for a class of BAM neural networks with time-varying delays of neutral type is concerned.The constructed Lyapunov functional depends on the lower and upper bounds of the time-varying delay.Delay-dependent conditions are established in terms of LMIs,which ensure the global stability for closed-loop error system.A numerical example with simulation results is provided to demonstrate the effectiveness of the proposed design method.4) New delay-dependent global robust stability conditions for interval neural networks with time-varying delays.The problem of delay-dependent global robust stability analysis for interval neural networks with time-varying delays is addressed.By introducing an equivalent transformation of interval systems and the free-weighting matrix technique,some new delay-dependent conditions on global robust stability are established.These conditions are presented in terms of linear matrix inequalities(LMIs),which can be easily checked by using recently developed algorithms in solving LMIs.A numerical example is provided to demonstrate the effectiveness of the proposed method.