The Robust Absolute Stability Of Stochastic Neutral Lurie Control Systems With Time-delay

Lurie system is a class of nonlinear system, it consists of a linear control system and a nonlinear term with feedback chaining. It is very important, because there are a lot of natural science and industrial design problems can be converted into Lurie control system to solve in the real world. Time-delay and stochastic noise interference are two general phenomena of our lives. In the process of the study,the stability of the systems will be declined no matter regardless of what kind of the problem. At present many scholars have studied neutral Lurie systems with time-delay. But the researches are very few in the stochastic neutral Lurie systems with time-delay. So the research of the stochastic neutral delay Lurie is valuable. Therefore, it is meaningful of the research about the stochastic neutral delay Lurie systems with multiple nonlinear actuators.This article mainly discuss and analyse the robust absolute stability of the stochastic neutral constant delay Lurie control system with multiple nonlinear actuators, the stochastic neutral constant delay Lurie control system with multiple nonlinear actuators and uncertain structure, the stochastic neutral time-varying delay Lurie control system with multiple nonlinear actuators, and the stochastic neutral time-varying delay Lurie control system with multiple nonlinear actuators and uncertain structure. First and foremost, we should construct the stochastic neutral delay Lurie control system with multiple nonlinear actuators. Secondly, constructing an appropriate Lyapunov function based on the system. Thirdly, according to the Lyapunov stability theorem, the sufficient condition of the system with constrained sector bounded to be robust absolute stability, expressed by the LMI, is obtained. Finally, few numerical examples are given to illustrate the results.