Stability proof for a well-established super-twisting parameter setting

Seeber, Richard; Horn, Martin

doi:10.1016/j.automatica.2017.07.002

Cited by 120 publications

(63 citation statements)

References 14 publications

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“…In addition, our further constructions also require a smoothness of Lyapunov functions. This is not the case for Lyapunov functions obtained in [20], [23], [24].…”

Section: B Global Asymptotic Lyapunov Stabilitymentioning

confidence: 86%

“…The finite-time stability of the closed-loop system (1) has been analysed in [20], [23], [24], where different Lyapunov functions have been exhibited. A crucial property to transport the Lyapunov stability properties from the continuous-time system to the discretized system, is that the (continuous-time) Lyapunov function has convex level sets.…”

Section: B Global Asymptotic Lyapunov Stabilitymentioning

confidence: 99%

“…A crucial property to transport the Lyapunov stability properties from the continuous-time system to the discretized system, is that the (continuous-time) Lyapunov function has convex level sets. It is not obvious that the Lyapunov functions proposed in [20], [23], [24] satisfy such a property (though some numerical calculations suggest that this could be the case). In addition, our further constructions also require a smoothness of Lyapunov functions.…”

Section: B Global Asymptotic Lyapunov Stabilitymentioning

confidence: 99%

See 2 more Smart Citations

The Implicit Discretization of the Supertwisting Sliding-Mode Control Algorithm

Brogliato

Polyakov

Efimov

2020

IEEE Trans. Automat. Contr.

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This paper deals with the analysis of the time-discretization of the super-twisting algorithm, with an implicit Euler method. It is shown that the discretized system is well-posed. The existence of a Lyapunov function with convex level sets is proved for the continuoustime closed-loop system. Then the global asymptotic Lyapunov stability of the unperturbed discrete-time closedloop system is proved. The convergence to the origin in a finite number of steps is proved also in the unperturbed case. Numerical simulations demonstrate the superiority of the implicit method with respect to an explicit discretization with significant chattering reduction.

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“…In addition, our further constructions also require a smoothness of Lyapunov functions. This is not the case for Lyapunov functions obtained in [20], [23], [24].…”

Section: B Global Asymptotic Lyapunov Stabilitymentioning

confidence: 86%

Section: B Global Asymptotic Lyapunov Stabilitymentioning

confidence: 99%

Section: B Global Asymptotic Lyapunov Stabilitymentioning

confidence: 99%

See 1 more Smart Citation

The Implicit Discretization of the Supertwisting Sliding-Mode Control Algorithm

Brogliato

Polyakov

Efimov

2020

IEEE Trans. Automat. Contr.

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“…One of the most popular continuous SMC for systems of relative degree one is the STA

\begin{matrix} right u & left = - k_{1} ⌊ σ ⌉^{1 / 2} + v, & right \\ right \dot{v} & left = - k_{2} ⌊ σ ⌉^{0}, \end{matrix}

where the gains depend on the Lipschitz constant Δ of the perturbation,

k_{1} > \sqrt{k_{2} + normalΔ}

and k 2 > Δ. Note that enforces the second‐order sliding‐mode in system when the actuator dynamics is fast enough ( μ = 0).…”

Section: Df Analysis Of Sliding‐mode Controllers For Systems With Relmentioning

confidence: 99%

When is it reasonable to implement the discontinuous sliding‐mode controllers instead of the continuous ones? Frequency domain criteria

Pérez‐Ventura

Fridman

2018

Intl J Robust & Nonlinear

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Summary Professor Utkin proposed an example showing that the amplitude of chattering caused by the presence of parasitic dynamics (stable actuators) in some systems governed by the First‐Order Sliding‐Mode Controller is lower than that produced by the Super‐Twisting Algorithm. This example served to motivate this paper reconsidering the problem of comparison of chattering in systems with stable actuators, and driven by Discontinuous Sliding‐Mode Controllers (DSMCs) and Continuous Sliding‐Mode Controllers (CSMCs). Comparison of chattering produced by DSMC and CSMC taking into account their amplitudes, frequencies, and average power (AP) needed to maintain the system into real‐sliding modes, allowing to conclude the following: (i) for systems with slow actuators, the amplitude of oscillations and AP produced by DSMC be smaller than those caused by CSMC; (ii) for bounded disturbances with fixed Lipschitz constant, there exist sufficiently fast actuators for which the amplitude of oscillations and AP produced by CSMC be smaller than those caused by DSMC.

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“…Its solutions are understood in the sense of Filippov [15]. The state-dependent dynamic matrix of system (7) can be written as…”

Section: A System Representationmentioning

confidence: 99%

The Robust Exact Differentiator Toolbox: Improved Discrete-Time Realization

Reichhartinger

Koch

Niederwieser

et al. 2018

2018 15th International Workshop on Variable Structure Systems (VSS)

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This paper presents a new release of A Robust Exact Differentiator Toolbox for Matlab/Simulink proposed in [1]. This release features a new discrete-time realization of the continuoustime robust exact differentiator. The implemented discretization scheme is less sensitive to gain overestimation and does not suffer from the discretization chattering effect. Hence, the single tuning parameter of the new version of the implemented differentiator is more intuitive to tune. Furthermore, it shows superior estimation performance in the case of large sampling times in comparison to the previous release. This is confirmed by the presented results obtained by numerical simulations and a real world application.

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Stability proof for a well-established super-twisting parameter setting

Cited by 120 publications

References 14 publications

The Implicit Discretization of the Supertwisting Sliding-Mode Control Algorithm

The Implicit Discretization of the Supertwisting Sliding-Mode Control Algorithm

When is it reasonable to implement the discontinuous sliding‐mode controllers instead of the continuous ones? Frequency domain criteria

The Robust Exact Differentiator Toolbox: Improved Discrete-Time Realization

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