Memoryless Output Feedback Control For A Class Of Stochastic Time-delay Nonlinear Systems

In recent years,the problem of nonlinear systems control has received an increased attention.Time delay and stochastic disturbance phenomena are unavoidable in application and may influence the stability of the systems.Hence,it is meaningful in theory and application to study the control of stochastic time-delay nonlinear systems.With the aid of feedback domination idea and Lyapunov-Krasovskii functional method,we design a memoryless output feedback controller for a class of stochastic time-delay nonlinear systems such that the closed-loop system is globally exponentially stable in mean square,then examples are given to show the effectiveness of the proposed control strategy.Due to the existence of time delay and stochastic disturbance,controller design and stability analysis become much more challenging.With the use of mean square exponential stability and theory of stochastic functional differential equations,this paper solve some difficulties mentioned in former papers.The main results of this paper are as follows:1.For a class of stochastic time-delay nonlinear systems with delays in the state and input,under upper-triangular form linear growth condition,we design a memoryless output feedback controller such that the closed-loop system is globally exponentially stable in mean square,no matter how large the input and state delays are;2.For a class of lower-triangular stochastic time-delay nonlinear systems with delays in the state and input,we design a delay-free output feedback controller such that the closedloop system is globally exponentially stable when input delay is limited.The controller designed in this paper is memoryless or delay-free which means the controller only depends on the current state of the system,hence,it is easy to implement.This paper shows not only the structure of the proposed output feedback controller,but also the existence of controller parameters.Moreover,this paper give the explicit expression of the gain L in the upper-triangular case.