Variable structure control design for reduced chatter in uncertain time delay systems

A variable structure control design methodology is proposed based on the concept of perturbation compensation to robustly stabilize time delay systems with nonlinear and possibly mismatched uncertainties. Sufficient robust stability conditions are derived and are shown to be independent of the size of the delay. Reduced chattering is attained as a direct benefit of perturbation compensation. The design does not need knowledge of uncertainty bounds, but it requires bounds on the error in estimating the derivative of the switching function. The results are illustrated with an open-loop unstable example