Abstract
The sliding mode control (SMC) problem for a normalized singular fractional-order system (SFOS) with matched uncertainties was investigated. Firstly, SFOS was normalized under constrained conditions. Then, the linear sliding mode (SM) function was designed using a fractional-order (FO) positive definite matrix and a linear matrix inequality (LMI). The SM controller was subsequently constructed based on switching laws. Finally, the feasibility of the method was evaluated using a numerical example.
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Acknowledgements
This work was supported by National Natural Science Foundation of China (Grant No. 61573008), Natural Science Foundation of Shandong Province (Grant No. ZR2016FM16), and Post-Doctoral Applied Research Projects of Qingdao (Grant No. 2015122). The authors would like to thank the anonymous reviewers for their valuable suggestions.
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Meng, B., Wang, X., Zhang, Z. et al. Necessary and sufficient conditions for normalization and sliding mode control of singular fractional-order systems with uncertainties. Sci. China Inf. Sci. 63, 152202 (2020). https://doi.org/10.1007/s11432-019-1521-5
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DOI: https://doi.org/10.1007/s11432-019-1521-5