Saturated Impulsive Stability Of Coupling Time-varying Systems And Its Application To Synchronization Of Neural Networks

In practical engineering,constraints exist widely and there are many types,among which saturation phenomenon is the most typical constraint behavior.In engineering control,if we ignore the impact of saturation constraints on system performance,it may cause system performance to decline or even crash.And for the time-varying system,the study about saturation control stability is more complicated,but its research results are few.Synchronizable coupled neural networks have a wide range of applications.Typical applications include confidential communication,storage of complex oscillation patterns,and management and control of large-scale networks.Therefore,in-depth exploration of saturation impulsive control theory and its application in coupled neural network exponential synchronization has high theoretical value and application significance.The main work of this article includes the following two aspects:(1)We study the saturation impulsive stability of coupled time-varying systems and proposed a full-state saturation-constrained impulsive controller.Under the impulsive controller,combining the theory of impulsive differential equations,convex analysis,and matrix measurement,and using constrained linear feedback impulsive controllers,some stability criteria are obtained to ensure the exponential stability of the coupled timevarying system.And theoretical analysis and proof of the proposed criteria are demonstrated.Finally,the validity of the theoretical analysis is verified by a numerical simulation.(2)The exponential synchronization of coupled neural networks based on saturation impulsive control is studied.In consideration of saturation,Two saturation impulsive control schemes are proposed: full saturation impulsive controller and partial saturation impulsive controller.When dealing with the actual saturation term,a sector nonlinear model method is used to construct several appropriate matrix inequalities(LMIS)conditions under the control of two impulsive constraints by constructing appropriate Lyapunov functions to ensure the index of the coupled neural network synchronize.The numerical simulation results verify the validity of the theoretical analysis.