A Lyapunov based Saturated Super-Twisting Algorithm

Castillo, Ismaël; Steinberger, Martin; Moreno, Jaime A.; Horn, Martin

doi:10.1007/978-981-15-8613-2_2

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2022

2024

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“…Notice that the flexibility of the Lyapunov approach allows the development of control algorithms to solve more particular problems. For saturated nonlinear systems, the work in [17] proposed a strong Lyapunov function to deal with the saturated super-twisting algorithm. Moreover, the implicit Lyapunov function methodology has also been applied to prove finite, and even more, fixed-time stability using the concept of homogeneity [18][19][20].…”

Section: Introduction 1motivationmentioning

confidence: 99%

Finite-Time Stability of a Second-Order Bang–Bang Sliding Control Type

et al. 2022

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This paper presents the double chain–integrator finite-time convergence in a closed loop with a second-order bang–bang sliding control. The direct Lyapunov method carried out the stability analysis and the reaching time estimation using a suitable non-smooth strong Lyapunov function. That is, the proposed energy function is strictly positive definite, with a strictly definite negative time derivative. Additionally, the proposed function estimates the reaching time in the presence of matching bounded perturbations. Numerical comparisons with well-known approaches were performed to assess the proposed strategy’s effectiveness.

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