Fixed-Time Synchronization And Control For Two Classes Of Coupled Nonlinear Systems

Synchronization of coupled nonlinear systems(CNSs)has been widely applied in different areas such as secure communication,image processing,model identification.Especially,in some engineering fields,it's always required that the synchronization of CNSs can be realized in finite time.Nevertheless,the settling time of the classical finite-time synchronization depends on the initial conditions of CNSs.It's not difficult to find that the settling time of the classical finite-time synchronization cannot be estimated when the initial conditions of CNSs are unavailable,which greatly reduce the practicability of the classical finite-time control technology.That's why the fixed-time synchronization and control is considered,where the setting time is independent of the initial values of CNSs.On the other hand,CNSs are inevitably affected by external uncertainties.So,in this paper,the fixed time synchronization and control of CNSs with uncertain factors including unmatched parameters,Markovian switching and stochastic disturbances is studied.The main contents are as follows:The second chapter investigates the fixed-time synchronization of four-dimensional nonlinear energy systems with mismatched parameters.By constructing a simple robust controller,combining with Lyapunov function method,fixed time stability theory and inequality technology,some synchronization conditions for this nonlinear system with or without mismatched parameters are given.Two numerical examples are given to illustrate the rationality of the results and the effectiveness of the designing controllerIn the third chapter,the issue of fixed-time synchronization for a class of coupled discontinuous systems with Markovian switching,uncertain parameters as well as stochastic disturbances is considered.By constructing an effective controller,designing comparison system and Lyapunov function,using M-matrix method,some synchronization conditions for this nonlinear system with or without Markovian switching,uncertain parameters as well as stochastic disturbances are given.A numerical example verify the validity of the conclusion.