Abstract
This paper discusses the sliding mode control (SMC) problem for nonlinear systems (NSs) with time-varying delays and external disturbances. Different from some existing results, the derivative of the time-varying delay is allowed to be bounded by an arbitrary bounded real number rather than by one. On this basis, an integral sliding mode surface (SMS) with time-varying delays is introduced. By exploiting the Lyapunov stability theory and the improved reciprocally convex inequality, several conditions of globally asymptotically stable are obtained for the sliding mode motion dynamics. Moreover, some results of globally exponentially stable are also established by resorting to double-integral calculations, the integral mean-value theorem and the zero-point existence theorem. Then, the normal/adaptive SMC laws are provided to ensure the reachability of the specified SMS. Finally, the validity and the application of the proposed SMC method are illustrated by two practical examples.
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