Abstract
• Higher order sliding mode definitions were formulated.
• It was shown that higher order sliding modes are natural phenomena for control systems with discontinuous controllers if the relative degree of the system is more than 1 or a dynamic actuator is present.
• A natural logic of actuator-like algorithm introduction was presented. Such algorithms also provide for the appearance of higher order sliding modes.
• Stability was studied of second order sliding modes in systems with fast stable dynamic actuators of relative degree 1.
• A number of examples of higher order sliding modes were listed. Among them the first example was presented of a third order sliding algorithm with finite time convergence. The discrete switching modification of this algorithm provides for the third order sliding precision with respect to the minimal switching time interval.
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Fridman, L., Levant, A. (1996). Higher order sliding modes as a natural phenomenon in control theory. In: Garofalo, F., Glielmo, L. (eds) Robust Control via Variable Structure and Lyapunov Techniques. Lecture Notes in Control and Information Sciences, vol 217. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0027563
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DOI: https://doi.org/10.1007/BFb0027563
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