Pole-placement in higher-order sliding-mode control

We show that the well-known formula by Ackermann and Utkin can be generalized to the case of higher-order sliding modes. By interpreting the eigenvalue assignment of the sliding dynamics as a zero-placement problem, the generalization becomes straightforward and the proof is greatly simplified. The generalized formula retains the simplicity of the original one while allowing to construct the sliding variable of a single-input linear time-invariant system in such a way that it has desired relative degree and desired sliding-mode dynamics. The formula can be used as part of a higher-order sliding-mode control design methodology, achieving high accuracy and robustness at the same time.