Robust stabilisation of distributed-order systems

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.