Abstract
This paper presents the design of a novel methodology for robust stabilisation of distributed‐order 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 pseudo‐state feedback, whose gain is adjusted by solving alinear matrix inequality. Since nonsmooth techniques induce not‐necessarily integer‐order differentiable solutions, the dynamical systems under consideration are defined through an operator that extends the distributed‐order differentiation of integer‐order differentiable functions to the case of not necessarily integer‐order differentiable ones. Numerical simulations highlight the reliability of the proposed scheme.