Razumikhin-type Approach On Output Feedback Control Of Nonlinear Systems With Time-varying Delay

In practical systems,non-linearity,time-delay and external random disturbance are ubiquitous,and time-delay is often an important factor that causes instability or oscillation of system performance.Therefore,the study of stochastic nonlinear systems and time-delay systems has received extensive attention.In this paper,the controller design and stability analysis for several different classes of time-varying delay nonlinear systems are studied.The main research results include:Using the backstepping design method of stochastic systems and the Razumikhin theorem,the output feedback stabilization problem of a class of second-order stochastic nonlinear systems with time-varying delay is studied.An effective observer is constructed by designing the gain function.Combined with the stability theory of stochastic systems,the output feedback controller ensures that the equilibrium point of the closed-loop system is globally asymptotically stable according to the probability.As the limitations of above design method,It can't spread to the output feedback stabilization of n-order system,so in the third chapter,when there is no random disturbance,the output feedback stabilization problem of a class of nonlinear time-varying delay system,by constructing suitable Lyapunov function,combined with the backstepping design method,etc.,and through inequality techniques and the incremental formula of binary function,obtained the research method of output feedback controller,and this method may also be applied to the n-order system,the designed output feedback controller makes the whole balance of the closed-loop system for global asymptotic stability in probability.By using the backstepping design method of stochastic systems,the Razumikhin theorem and the full increment formula of the element function,the stochastic time-varying delay system is extended to n-order,and the output feedback stabilization problem is studied.The designed output feedback controller ensures that the entire closed-loop system is globally asymptotically stable in probability.In the above three parts,the simulation examples can verify the effectiveness of the control scheme.