Stability,Instability And Stabilization Of Random Nonlinear Time-Delay Systems

The random nonlinear systems with time-varying delay,which consider both stochastic disturbance(colored noise)and time delay,is an important mathematical model.And it has been widely used in cybernetics,neural networks,finance and other fields.Based on this,this paper investigates a class of random nonlinear time-delay systems driven by -order processes.The stability,instability and stabilization of this system are considered.Firstly,based on locally Lipschitz conditions,the existence and uniqueness of solutions to random nonlinear time-delay systems are analyzed in this paper by using the uniformly asymptotically stable function.And some theorems about existence and uniqueness of solutions to this system are given.Secondly,on the basis,make good use of Young's inequality and Fubini's theorem,some new criteria of noise-to-state stability are established in the mth moment sense and in probability sense,respectively.And some examples verify the effectiveness of the obtained findings,which show that the stability theorems presented in this paper relax the restrictions in the existing classical approaches by using the uniformly asymptotically stable function.Then,this paper investigates the instability of random nonlinear time-delay systems.By means of the uniformly asymptotically stable function,some sufficient conditions,that guarantee this system is mth moment exponentially unstable and mth moment unstable,are derived respectively.At last,in view of the stabilization,we study stabilization of random nonlinear systems using a linear state-feedback control first.Then a similar way is adopted to investigate the stabilization problem of random nonlinear time-delay systems.With the help of the uniformly asymptotically stable function,the criteria of exponential stability in mth moment are constructed for the obtained controlled system.