Synthesis of an Optimal Sliding Function Using LMIs Approach for Time Delay Systems

During the reachability phase, the sliding mode control is sensitive to external disturbances and uncertainties. In this paper, we propose to determine coefficients of the sliding function using the technique of Linear Matrix Inequalities (LMIs) for single-input single-output time delay systems. This technique leads to an optimal choice of the sliding function to reduce the reachability phase. Using the proposed sliding function, a discrete second order sliding mode control is presented. The control law is based on an input–output model. Simulation results demonstrate that the proposed strategy leads to an optimal performance in terms of reduction of the reachability phase as well as the chattering phenomenon.

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