Projective synchronisation of variable-order systems via fractional sliding mode control approach

This study concerns with the projective synchronisation problem of fractional variable-order master–slave systems via the fractional sliding mode control. Firstly, an applicative index law is designed for the considered fractional variable-order system based on the Grünwald–Letnikov definition. Secondly, two different fractional variable-order sliding surface functions are proposed to study this projective synchronisation problem. Meanwhile, sufficient conditions are obtained to ensure the projective synchronising error is asymptotically stable. Finally, numerical examples show the validity and feasibility of the proposed approach.