Optimal discrete-time integral sliding manifold design for linear systems subjected to a class of unmatched disturbances

This paper proposes a design method of the discrete-time integral sliding manifold that minimizes linear systems sensitivity to unmatched constant or slowly-varying external disturbances. The impact of unmatched disturbances is evaluated by a steady-state dependent quadratic criterion. An efficient design procedure is derived that easily finds the optimal sliding manifold that minimizes a criterion in discrete-time integral sliding mode control system. The suggested approach has been verified on numerical examples and computer simulations.