This paper presents the design of a novel methodology for robust stabilisation of distributedorder systems, which are subject to both matched and mismatched disturbances. Matched disturbances are coped through a nonlinear controller, while mismatched disturbances are rejected by a pseudostate feedback, whose gain is adjusted by solving alinear matrix inequality. Since nonsmooth techniques induce notnecessarily integerorder differentiable solutions, the dynamical systems under consideration are defined through an operator that extends the distributedorder differentiation of integerorder differentiable functions to the case of not necessarily integerorder differentiable ones. Numerical simulations highlight the reliability of the proposed scheme.
