Fractional inverse full state hybrid projective synchronisation

Referring to fractional-order systems, this paper investigates the inverse full state hybrid projective synchronisation (IFSHPS) of non-identical systems characterised by different dimensions and different orders. By taking a master system of dimension n and a slave system of dimension m, the method enables each master system state to be synchronised with a linear combination of slave system states, where the scaling factor of the linear combination can be any arbitrary real constants. Based on fractional Lyapunov approach and stability theory of linear fractional-order systems, the method enables commensurate and incommensurate fractional-order systems with different dimension to be synchronised. Two different numerical examples are reported. The examples clearly highlight the capability of the conceived approach in effectively achieving synchronised dynamics for any scaling constants.