Stability Of Neural Networks With Time-varying Impulses

The most prominent feature of impulse control strategy is that it can fully consider the impact of instantaneous phenomena on the state of the systems,and it can reflect the changing rule of objects more accurately.Furthermore,it is widely applied in practice owing to its easy generation and low control cost.At present,most of the research results are based on fixed-time impulse control strategy.However,the time of impulse triggering cannot be completely accurate or predicted in advance in physical circuits,biological systems,chemical reaction processes,et al When impulse controllers are designed,researchers tend to apply time intervals which satisfy the impulse triggering instead of the fixed impulse instants according to their experience,so that the time complexities of the algorithm will be reduced effectively.Therefore,the time-varying impulse control strategy can better meet the needs of the actual systems.In recent years,it is a hot topic to apply time-varying impulse control strategy to study the dynamic characteristics of neural networks.Based on the existing research achievements,the study focuses on the stability of neural networks with time-varying impulsive control.The main contents and innovations of this thesis include the following aspects:1.Fixed-time impulses of classical theories are extended to the "impulse time wind ow",that is,impulses are no longer confined to accurate instants,but are allowed to trigger in certain time intervals randomly.The stability of Hopfield neural network is studied under the condition.By applying impulse control theories,Lyapunov stability theories and mathematical induction,sufficient conditions for the global exponential stability of the neural networks are obtained.The effectiveness of the theoretical results is verified by two simulation examples.2.Based on the "impulse time window" control strategy,taking the effects of discrete and distributed time delays on the system into consideration,combined with the dynamic characteristics of memristor devices in the meantime,the stability of Cohen-Grossberg neural networks is studied.By applying impulse control theories,integral inequalities,mathematical induction method and constructing several Lyapunov functions,sufficient conditions for the global exponential stability of the Cohen-Grossberg neural networks with mixed time delays are obtained.Furthermore,the impact of impulse frequency and intensity on system stability is analyzed as well.A numerical simulation example is given to verify the validity of the theoretical results.3.The global exponential stability of nonlinear systems with time-varying impulsive control is studied.Based on several reasonable assumptions,we first ensure that each solution of the system intersects with the discontinuous surface exactly once,then the nonlinear system with time-varying impulsive control is reduced to a fixed-time impulsive nonlinear system by applying the B-equivalence method.By means of comparison principle,the comparison system of the time-varying impulse system is obtained,and the stability of the comparison system is analyzed.Through strict derivation,it is concluded that the time-varying impulse control system has the same stability as the corresponding fixed-time impulse system.A set of stability criteria is established,and the validity of the theoretical results is verified by a simulation example of Chua's circuit.4.The global exponential stability of state-dependent impulsive Hopfield neural networks is studied.By applying B-equivalence method,mathematical induction,counter-proof and Gronwall-Bellman's inequality,et al,the state-dependent impulsive Hopfield neural networks are transformed into the fixed-time impulsive neural networks,and the global exponential stability conditions of the corresponding comparison system are obtained,so that the theoretical framework for analyzing the stability of Hopfield neural networks is established.In view of three different situations,the corresponding impulse control strategies are proposed to obtain sufficient conditions for the stability of Hopfield neural networks.The effectiveness of theoretical results is verified by three simulation examples.