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In this technical note, a local stabilization problem for nonlinear systems with disturbances which are dependent on time-varying delay phenomena, is studied. An appropriate transformation is introduced to express the system in regular form which facilitates both design and analysis. Then, sufficient conditions are developed based on a Lyapunov-Razumikhin approach such that the sliding motion is uniformly asymptotically or exponentially stable. A static output feedback control law, independent of the time delay, is synthesized to guarantee reachability of the sliding mode. The accessible bounds on the disturbances are fully used in the control design to reduce the conservatism. A simulation example shows the effectiveness of the approach.
Yan et al. (Fri,) studied this question.