Stabilisation of commensurate fractional‐order polytopic non‐linear differential inclusion subject to input non‐linearity and unknown disturbances

In this study, a fractional‐order adaptive‐sliding mode control (SMC) scheme is proposed to stabilise commensurate fractional‐order polytopic non‐linear differential inclusion systems containing sector and dead‐zone nonlinearities in the control inputs and unknown bounded disturbances. The suggested control method is composed of fractional‐order sliding surfaces, adaptive‐SMC inputs and adaptation laws for unknown bounds of disturbances. The Lyapunov stability theorem is used to prove the stability of the closed‐loop system. A practical system and two numerical examples are simulated to show the effectiveness and performance of the proposed control technique.