Research On The Sliding Mode Control Of Time-delay System With Uncertainty

The uncertainty and time delay in real systems will reduce the system performance and even cause the system instability.Therefore,the study of the stability and control methods of uncertain time-delay systems is of great theoretical significance and practical value.Sliding mode variable structure control(SMVSC)is robust to external disturbances and changes of system parameters,which has been proved in many kinds of systems.Based on sliding mode control theory,Lyapunov Stability Theorem,Linear Matrix Inequality theory and adaptive theory,three kinds of time-delay systems are analyzed and concrete control schemes are designed.(1)Adaptive sliding mode control method based on neural network is proposed for timedelay systems with parameter perturbations and uncertain disturbances.Based on time-delay segmentation,the Lyapunov-Krasovskii functional(L-K functional)is constructed using the available time-delay information.Then,the asymptotic stability condition of the nominal system is obtained by means of the Wirtinger integral Inequality,and the asymptotic stability condition is expressed by the Linear Matrix Inequality(LMI).In addition,for the external disturbance and uncertainty in the system,the neural network approach is adopted,and the combination of sliding mode control and neural network control ensures the stability of the closed-loop system.(2)For the neutral time-delay system with external disturbance,input nonlinearity and uncertainty,the state of the system is reconstructed when the state is unknown or the state is difficult to measure or can not be measured.Then an adaptive sliding mode controller is designed based on the state estimation obtained by the state observer.The controller gain and observer gain are obtained by LMI.The closed-loop system is asymptotically stable under the designed controller,and the adaptive method solves the problem of unknown upper bound of system disturbance.(3)This paper deals with nonlinear singular time-delay systems with uncertainties in derivative matrix.Firstly,the state augmentation technique is used to guarantee the robust passivity.Then,an integral sliding surface with sliding mode gain matrix is constructed,and by designing appropriate L-K functional,new sufficient conditions are obtained to guarantee the quadratic stability of the sliding mode and passivity.At the same time,the sliding mode control law is designed to make the system trajectory reach the preset sliding mode surface in a certain time.