Exponential Stability For Some Classes Of Nonlinear Switched Neural Networks With Time Delays

As an important type of complex networks."Switching Neural Networks(SNNs)" is a system composed of continuous dynamic system and discrete switching signal.Owing to external disturbances and other networked factors,the system state may change at switching time.In this thesis,we study the stability of a class of switching neural networks with partial state reset,that is,only a fraction of the states can be reset at each switching instant.For example,in network congestion control,applying "caching" to switches is an effective way to avoid network congestion and thereby optimizing quality of service.The principle of"caching" is to maintain the states of a fixed number of flows by processing a part of the system states,so as to contain the unresponsive flow and provide fair bandwidth distribution for data streams.At present,due to the difficulty in modeling and theoretical analysis,the results concerning the stability of switched neural networks with partial state reset are limited,and the stability problem needs to be solved urgently.Therefore,based on the existing results of the switching system,in this thesis,we firstly propose a new switching law to model the phenomenon of partial state reset of the system at the switching instant,then by proposing a time-dependent Lyapunov function,using Lyapunov stability theorem,comparison principle and inequality technique,the stability was studied for SNNs with partial state reset.Moreover,the estimation was given for the value of time delay and the switching law to make the switched systems stable.The main content of this thesis is as follows:The first chapter introduces the research background and current research status of the stability of SNNs at home and abroad.At the same time,the main research contents and the contributions of this thesis are provided.The second chapter considers the exponential stability of SNNs with both stable and unstable subsystems.Most existing literature focus on the total state reset,the results concerned with partial state reset has received relatively little attention.In this thesis,firstly,a new model is proposed to model SNNs with stable and unstable subsystems and partial state reset,then,sufficient conditions are obtained to ensure that the considered delayed SNNs with partial state reset are exponentially stable.Subsequently,the validity of the theoretical results in this thesis is verified by several numerical examples.In the third chapter,based on the previous results,the synchronization was investigated for coupled SNNs with partial state reset,that is,only part of the states of each node in the network can be reset at the switching instants,which shows that our results can be applied to the pinning control of complex networks.