Sliding mode control of retarded nonlinear systems via finite spectrum assignment approach

In this study, a sliding mode control design method based on the finite spectrum assignment procedure is proposed. The finite spectrum assignment for retarded nonlinear systems can transform retarded nonlinear systems into delay-free linear systems by using a coordinates transformation and a feedback, which contain the past values of the state. This method can be considered as an extension of both the finite spectrum assignment for retarded linear systems with controllability over polynomial rings of the delay operator and the exact linearization for finite dimensional nonlinear systems. The proposed method here is to design a sliding surface by using the coordinates transformation used in the finite spectrum assignment and to derive a switching feedback law. The obtained surface contains not only the current values of the state variables but also the past values of the state variables in the original coordinates. Effectiveness of the proposed method is tested by an illustrative example.