Projective synchronisation of variable-order systems via fractional sliding mode control approach. (English) Zbl 07907030
Summary: 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.
© 2021 The Authors. IET Control Theory & Applications published by John Wiley & Sons, Ltd. on behalf of The Institution of Engineering and Technology
© 2021 The Authors. IET Control Theory & Applications published by John Wiley & Sons, Ltd. on behalf of The Institution of Engineering and Technology
MSC:
| 93B12 | Variable structure systems |
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 34A08 | Fractional ordinary differential equations |
| 93D20 | Asymptotic stability in control theory |
Keywords:
synchronisation; variable structure systems; variable-order master-slave systems; applicative index law; considered fractional variable-order system; Grünwald-Letnikov definition; different fractional variable-order; projective synchronisation problem; projective synchronising error; variable-order systems; fractional sliding mode control approachReferences:
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