Robust control of nonlinear time delay system: a sliding mode control design

摘要

This paper outlines a sliding mode control of nonlinear uncertain systems, linear in the control, with single, possibly time-varying state-delay. These systems are submitted to additive perturbations (possibly nonvanishing). The sliding surface is designed to maximize the calculable set of delays which do not destabilize the relay-delay system. The conditions for the existence of the sliding regime are studied by using both a Liapunov Krasovskii functional and a Liapunov-Razumikhin function. The optimization procedure for the choice of the sliding surface are expressed in terms of LMIs. An example illustrates the proposed method.