Sliding-mode control design for a complex valued sliding manifold

This paper gives precise conditions for the existence of a state feedback sliding-mode controller to achieve a complex, closed-loop eigenstructure. This structure can be advantageous in providing maximum flexibility in specifying closed-loop dynamics. It is found that the controller is inherently dynamic in general, and recovers standard sliding-mode control results when all real elements are chosen for the switching surface matrix. A control design algorithm is presented, and robustness of the resulting closed-loop system is demonstrated. An illustrative example is provided.