This paper proposes an nth‐order suboptimal integral sliding mode controller for a class of nonlinear affine systems. First, a general form of integral sliding mode is given. An extended Theta‐D method is developed for the optimal control problems characterized by a quadratic cost function with a cross term. Then the extended Theta‐D method is employed to determine a suboptimal integral sliding mode. Rigorous proof shows that the controller guarantees semi‐global asymptotical stability of affine systems. To verify the accuracy of the extended Theta‐D method, a numerical example is provided. To verify the effectiveness of the proposed suboptimal integral sliding mode controller, a numerical example and an application example of an overhead crane system are provided.
