Stabilization Of Nonlinear Time-delay Systems Based On Static Gain Functions

With the rapid progress of science and technology,only mastering the traditional control meth-ods can not meet the needs of social development in recent years.Especially the application devel-opment of artificial intelligence and the widespread popularity of network technology have opened up a broad world for the application of modern control theory.However,the most prominent problem in the field of control is the time delay phenomenon,which generally exists in biological systems,network control systems,process control systems and other aspects.It is well known that time delay will lead to system performance degradation and even system instability.On the other hand,due to environmental changes,measurement errors and modeling errors,real systems often encounter significant uncertainties.Therefore,how to reduce the influence of time delay and uncertainty on the stability and control performance of the system has important theoretical and practical significance.On the basis of the existing literature,some work is done on the stability analysis and control of uncertain nonlinear time-delay systems.For a class of nonlinear systems with mismatched time delays and external disturbances,ro-bust adaptive stabilization control is addressed.A new control gain function is firstly defined,and its useful properties are presented.By introducing a new Lyapunov-Krasovskii functional with explicit control gain expression,we develop a novel memoryless control strategy.The control law is split into two terms.One is used to cope with the delayed states,and the other is to han-dle the disturbance.The role of control gain function is to suppress the addition term resulted by the derivative of Lyapunov-Krasovskii functional.The improved adaptive laws with control gain function and time-varying ?-modification are constructed to estimate the unknown integrated parameters.A nonlinear time-varying time-delay system based on the output feedback control of the ob-server is studied.When the state information of the system is unmeasurable,the Luenberger ob-server is constructed to estimate the state,and then two continuous positive functions are defined.At the same time,Lyapunov-Krasovskii functional is used,and two constants are introduced to deal with the mismatches of the system.In order to deal with the sub-part information of the sys-tem state,we discuss a new state estimation equation,therefore design a new controller,and the condition of asymptotic stability for the nonlinear system with time-varying delay is obtained.