A new algorithm for high‐order sliding mode control

A new robust high‐order sliding mode controller for a class of uncertain minimum‐phase single‐input–single‐output (SISO) nonlinear systems is designed. The high‐order sliding mode problem is formulated in input–output term and is viewed in uncertain linear context by considering uncertain nonlinear functions as bounded non‐structured parametric uncertainties. A sliding manifold is designed in order to ensure finite‐time convergence of sliding variable and its high‐order time derivatives. The control law allows the establishment of an r th‐order sliding mode. This result is extended to multi‐input–multi‐output (MIMO) systems.