Abstract
The initial ideas for designing systems with a sliding mode were formulated half a century ago for dynamic models in canonical space with scalar input and output. The interest in the behavior analysis in the space of the output variable and its time derivatives was explained by the property of invariance with respect to perturbations and parametric variations. This invariance property is lost for arbitrary space in systems with vector input and output, which predetermined the need for new mathematical methods for the analysis of such systems and design of control methods with sliding modes. The set of these questions is the content of this book.
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Notes
- 1.
We follow the terminology: “conventional” means the first-order sliding mode, “new” means the high-order sliding mode. The term “conventional SMC” appeared in Shtessel et al. (2014), for the first time. The details will be discussed in the subsequent chapters.
References
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Utkin, V.: Variable structure systems with slidnng mode control. IEEE Trans. Autom. Control 22(2), 212–221 (1977)
DeCarlo, R., Zak, S., Matthews, G.: Variable structure control of nonlinear multivariable systems: a tutorial. Proc. IEEE 76(3), 212–232 (1988)
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Utkin, V., Poznyak, A., Orlov, Y.V., Polyakov, A. (2020). Introduction. In: Road Map for Sliding Mode Control Design. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-41709-3_1
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DOI: https://doi.org/10.1007/978-3-030-41709-3_1
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