Sliding Mode Control For Uncertain Time-Delay Systems

Sliding mode control is an effective robust control method, when the system enters the sliding mode motion, it has adaptiveness or invariance to the disturbance and parameter uncertainty. This paper studied the stability of the uncertain control systems with time-delays. Based on the Lyapunov function method, using linear matrix inequalities (LMI) method, we studied the asymptotic stability of uncertain systems and the global sliding mode control problems.Briefly introduced the development of sliding mode control, the development and the current research results of switched system, research of sliding mode control for switched systems; Introduced the basic content of switched systems and sliding mode variable structure control.Discussed the global sliding mode control problems for a class of uncertain systems with input time-delay. It gave the design process of the global sliding mode control. Based on the Lyapunov function method, using linear matrix inequalities (LMI) technology, we proved the existence of sliding mode, asymptotic stability and reaching conditions. Controllers were designed; they can ensure the asymptotic stability of the system. A simulation was given at last.Discussed the global sliding mode control problems for a class of uncertain systems with state time-delay, firstly, the non-singular linear transformation was given, and the original system became a linear system without delay. It gave the design process of the controller and integral sliding mode surface, by using Lyapunov function method and linear matrix inequalities method, we obtained sufficient conditions for asymptotic stability of sliding mode, and verified a sufficient condition for the asymptotic stability of the original system. At last we gave a simulation.The problem of designing the global sliding mode controllers for a class of uncertain switched system with input and state time-delay was considered. A linear transformation was defined to transform the original system into state-delay form. We gave the sliding surface and the controller of each subsystem, and on this basis, gave the design process of sliding mode control for the system, we obtained the sufficient condition for asymptotic stability of sliding mode under arbitrary switching. At last, we gave a simulation.