Stability Analysis Of Several Discontinuous Models With Time Delay

Discontinuous models are characterized by discontinuous differential equations at the right end,which often appear in neural networks,biology,dynamic economics,mechanical engineering,electrical engineering and other fields.The stabilization control of the right-hand discontinuous model is one of the new and important research topics in the field of differential equations and dynamical systems.The purpose of this thesis is to use modern mathematical knowledge(such as the extended differential inclusion theory,Lyapunov function method,finite time stability theorem,fixed time stability theorem,and exponential synchronization theorem,etc.)to study the stability control problem of discontinuous model with time delay by designing some appropriate discontinuous controllers and then to use the obtained results to study the dynamical models in the fields of state economics,neural network and biology,which provides practical and reliable theoretical basis methods for researchers in related application fields.The research of this project extends and complements the exist results on stability predictive control in dynamic economics,neural network and biology.In the first chapter,we mainly introduce the research significance and development status of the right-hand discontinuous differential equation,and briefly summarize the results of this paper.Finally,we also give the preliminary knowledge needed.In the second chapter,we establish a right-hand discontinuous model with time delay for the discontinuous price system.Under three different controller,we state some associated sufficient criteria to ensure the finite time stability of such a system.Moreover,we can also estimate the upper bound of finite time convergence.In the third chapter,we establish a matrix model of time-delay gene regulatory network,and study the fixed time stability control of the error system of the delayed gene regulatory network.Besides,we also give the time estimation of the fixed time stable control of the model.In the fourth chapter,we study the exponential synchronization control problem to a class of fuzzy neural network model with time delay.By using the master-slave system,we establish a new criterion to realize the exponential stability of the error system,and then to achieve the global exponential synchronization of the master-slave system.