Sliding Manifold Design for Higher-order Sliding Mode Control of Linear Systems

The paper considers sliding manifold design for higher-order sliding mode (HOSM) in linear systems. In this case, the sliding manifold must meet two requirements: to achieve the desired dynamics in HOSM and to provide the appropriate relative degree of the sliding variable depending on the SM order. It is shown that in the case of single-input systems, a unique sliding manifold can be determined that satisfies these two requirements, whereas in multi-input case, such a manifold exists only in systems satisfying specific structural constraints. Theoretically obtained results are validated through numerical examples and illustrated by digital simulations.