Robust Control of Nonlinear Time Delay System: A Sliding Mode Control Design

Abstract 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 relaydelay system. The conditions for the existence of the sliding regime are studied by using both a Liapunov Krasovskii functionnal 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.

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