Analysis And Control Of Logical Dynamic Systems With Impulsive Effects

With the rapid development of medical science and systems biology,logic sys-tem with impulsive effects has been widely studied as an important model of gene regulatory networks.Using the algebraic state space representation method,this pa-per studies the stability,stabilization of logic systems with impulsive effects.Firstly,the semi-tensor product of matrices method is used to convert the logic system with impulsive effects into a linear form,then classical control theory can be used to study logic systems with impulsive effects.Secondly,the stability and stabilization of logic dynamic systems with impulsive effects are redefined in the dynamic system based on trajectory.Through mathematical induction,the sufficient and necessary conditions for stability and stabilization of logic dynamic systems with impulsive effects are studied.Moreover,the stability analysis is further extended and the stochastic stability problem is studied under the cases of stochastic switching sig-nal and Markov jump switching signal Thirdly,as applications,output tracking and synchronization,including state synchronization and output synchronization,are studied.Finally,some numerical examples and diagrams are used to verify the validity of the theoretical results.