Universal single-input-single-output (SISO) sliding-mode controllers with finite-time convergence

By Arie Levant. IEEE Transactions on Automatic Control, 2001

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Guidance Laws with Finite Time Convergence (2009, background): “Examples include 1) finite time stability based on Lyapunov and converse Lyapunov results involving scalar differential inequalities [21], 2) finite time stability of a guidance system [22], 3) arbitrary-order sliding-mode controls with finite time convergence [23], and 4) guidance laws with finite ”
New methodologies for adaptive sliding mode control (2010, methodology): “A second way to decrease the chattering phenomenon is the use of higher order sliding mode controller (Levant 1993, 2001, 2007; Bartolini, Ferrara, Usai, and Utkin 2000; Laghrouche, Plestan, and Glumineau 2007; Plestan, Glumineau, and Laghrouche 2008).”
Chattering free full-order sliding-mode control (2014, methodology): “A number of methods for attenuating chattering have been proposed, such as boundary layer method (Utkin, 1992), high-order sliding-mode method (Bartolini, Ferrara, & Usai, 1998; Levant, 1998, 2001, 2005, 2007), and disturbance estimation method (Shtessel, Shkolnikov, & Brown, 2003).”
On optimal predefined‐time stabilization (2017, background): “Recall that there is a direct connection between the notions of relative degree and sliding order [44].”