Input-to-state Stability For Stochastic Delay Neural Networks With Markovian Switching

In this thesis,mainly studies the p(p ≥ 2)moment input-to-state stability,p(p ≥2)moment integral input-to-state stability,and almost inevitable exponential input-tostate stability of stochastic non-autonomous neural network with time-varying delay and Markovian switching.In order to overcome the difficulties brought by the existence of bounded variable delay,the input-to-state stability of this network is studied by establishing delay integral inequality and using the Lyapunov function method and stochastic analysis theory.Specifically,the specific chapters of this paper are as follows:In chapter one,this paper mainly introduces the research background,research significance,research problems and some preliminary knowledge.In chapter two,when bounded time-varying delays and time-varying coefficients with invariant sign in Lyapunov monotonicity condition,one generalized delay integral inequality is established;When there are time-varying coefficients with variable sign in Lyapunov monotonicity condition,another generalized delay integral inequality is established.Using Lyapunov function and stochastic analysis theory,the p(p ≥ 2)moment input-to-state stability,p(p ≥ 2)moment integral input-to-state stability and almost inevitable exponential input-to-state stability of stochastic non-autonomous timevarying neural networks with Markovian chains are discussed.The sufficient conditions based on algebraic inequality and integral inequality have been given.In chapter three,when distributed time-varying delays and time-varying coefficients with invariant sign in Lyapunov monotonicity condition,a generalized delay integral inequality is established.Using Lyapunov function and stochastic analysis theory,the p(p ≥ 2)moment input-to-state stability,p(p ≥ 2)moment integral inputto-state stability and almost inevitable exponential input-to-state stability of stochastic non-autonomous neural networks with Markovian chains and distributed variable delays are discussed.Sufficient conditions based on algebraic inequalities have been given.In chapter four,summary and prospect.