Abstract

In this paper, the problem of robust stability of fractional-order nonlinear systems under sliding mode control (SMC) with fractional-order (FO) switching law is discussed. The proposed FO switching law, involving an FO derivative function, is proven to guarantee that the reaching phase can happen in finite time. The calculation formula of the reaching time is computed. The comparisons between FO and integer-order (IO) switching laws reveal the potential advantages of one controller over the other. The stability criterion of the sliding mode dynamics is derived in terms of linear matrix inequalities (LMIs). The tradeoff between control performance and parameters selection is discussed and visualized. Simulation results are presented to illustrate the effectiveness of the designed FO SMC.

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