Stability notions and Lyapunov functions for sliding mode control systems

By Andrey E. Polyakov, Leonid M. Fridman. Journal of the Franklin Institute, 2014

425 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/3727208b52d6236d1068def5b7f817edc34f918d

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In Control and Systems Engineering

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Citations in the corpus

A class of predefined-time stable dynamical systems (2018, positive): “To make the settling time bounded for any initial condition a stronger form of stability, called fixed-time stability, was introduced by Andrieu et al. (2008) for homogeneous systems and by Cruz-Zavala et al. (2010), Polyakov (2012), Polyakov and Fridman (2014) for systems with sliding modes.”
A fixed-time output feedback control scheme for double integrator systems (2017, background): “In this case, the solutions of (1) are understood in the sense of Filippov [21,22].”
Fixed-time backstepping control design for high-order strict-feedback non-linear systems via terminal sliding mode (2017, background): “In addition, even though in the above literatures the finite-time stability is proved [10] and the settling time functions are also derived, it should be noticed that the settling time functions derived with finite-time control depend on system initial states [11–13], i.”
Sliding-Mode-Based Differentiation and Its Application (2017, background): “…equals r, and the output can be in finite time stabilized at zero by means of the rthorder SM (r-SM) (Bartolini et al. (2003); Floquet et al. (2003); Levant (1993, 2003); Man et al. (1994); Moreno and Osorio (2012); Polyakov and Fridman (2014); Shtessel and Shkolnikov (2003); Yang and Yang (2011)).”
A Lyapunov-Like Characterization of Predefined-Time Stability (2019, background): “In the same manner, they have been highly used for the convergence rate estimation in systems exhibiting finite- and fixed-time stability properties [4], [8], [13], and in particular in systems with sliding modes (SM) [14].”
Finite-time and fixed-time stabilization: Implicit Lyapunov function approach (2015, methodology): “Finally, we finish the proof using Theorem 4.1 from Bacciotti and Rosier (2005) and, for example, Lemmas 4, 6 from Polyakov and Fridman (2014).”
Time-varying feedback for regulation of normal-form nonlinear systems in prescribed finite time (2017, methodology): “Prescribed regulation time T is achievable with such non-smooth approaches by suitably adjusting their gains based on the initial condition following the guidance by Polyakov and Poznyak (2009) and in Theorem 13 by Polyakov and Fridman (2014).”
An Overview of Recent Advances in Fixed-Time Cooperative Control of Multiagent Systems (2018, neutral): “ble systems [32].”