Robust predictor-based sliding modes control for nonlinear time-delay systems via Takagi-Sugeno approach

In this paper a novel discontinuous control strategy for robust stabilization for a class of uncertain nonlinear time-delay systems with delays in both the state and control variables is proposed. First, a Takagi-Sugeno technique is used to approximate the nonlinear system by a set of linear subsystems. Then, two predictors are used to compensate the control input delay, and in the following a super-twisting control algorithm is applied. The super twisting algorithm ensures robustness with respect to external disturbances and unmodeled dynamics resulting from the linearization of the nonlinear systems while reducing the chattering effects. Finally, a nominal free-delay part of the control input using LMI'S technique is designed to stabilize the sliding mode dynamics. Conditions for the stability of the closed-loop perturbed system are derived. An example illustrates the applicability of the proposed scheme.