Sliding Mode Control For Uncertain Systems With Time-Delay

In actual process of industry, time-delays and uncertainties are very common invarious systems, they’re also two of the important factors which lead to instability.Therefore, it’s very important to research the uncertain control systems withtime-delays and the study has very important value in practice. Sliding mode controlhas self-adaptabilty of the uncertainty for internal parameters and externaldisturbances, it’s a very effective control method. Because of this, it has a strongappeal to the researchers. In this paper, we consider the sliding mode variablestructure control problem of uncertain systems with time-delays.The main content is summarized as follows：Firstly, simply introduce the development history of sliding mode control and thedevelopment history of variable structure control for discrete-time systems, brieflyintroduce the elementary definitions, the elementary methods and design method ofsliding mode control.Secondly, the slide mode control problem is considered for a class of variabletime-delay system. There exist many variable time-delay and uncertainties. Using theLyapunov method and the Schur Complement Lemma, the stability of the slide modeis demonstrated. A variable structure controller is designed, which is more easy andefficient. It makes the system’s state trajectories can be ensured to reach the chosenslide mode surface at initial time and keep on the slide mode surface. Simulationresults demonstrate the effectiveness of the presented method.Thirdly, the slide mode control problem is considered for a class of multy-delaydiscrete-time system. First, by using the linear matrix inequalities method, proceedlinear transformation for the system, the slide mode surface is designed for the system.Based on the Lyapunov function method, the stability of the slide mode is proved.Then, the controller is designed to make sure the state of the system will arrive at theslide mode. Last, it gives the corresponding controller and the correspondingsimulation example.Fourthly, the slide mode control problem is considered for a class of uncertaindiscrete-time systems with input and state delays. First, by using two time lineartransformation for the system to transform the original system into a linear systemwithout delay. Then the slide mode surface and the control law are designed for thesystem without delay, the stability for the system is discussed, and the simulationexample is given for the system.