Construction of a smooth Lyapunov function for the robust and exact second-order differentiator
type: Item
instance of: scholarly article
title: Construction of a smooth Lyapunov function for the robust and exact second-order differentiator
zbMATH Open document ID: 1400.93094
DOI: 10.1155/2016/3740834
author: Tonametl Sanchez
author: Jaime A. Moreno
author: Fernando A. Ortiz-Ricardez
published in: Mathematical Problems in Engineering
publication date: 2018-10-12T00:00:00Z
review text: Summary: Differentiators play an important role in (continuous) feedback control systems. In particular, the robust and exact second-order differentiator has shown some very interesting properties and it has been used successfully in sliding mode control, in spite of the lack of a Lyapunov based procedure to design its gains. As contribution of this paper, we provide a constructive method to determine a differentiable Lyapunov function for such a differentiator. Moreover, the Lyapunov function is used to provide a procedure to design the differentiator's parameters. Also, some sets of such parameters are provided. The determination of the positive definiteness of the Lyapunov function and negative definiteness of its derivative is converted to the problem of solving a system of inequalities linear in the parameters of the Lyapunov function candidate and also linear in the gains of the differentiator, but bilinear in both.
Mathematics Subject Classification ID: 93B52
Mathematics Subject Classification ID: 93B12
Mathematics Subject Classification ID: 93D05
Mathematics Subject Classification ID: 94C30
zbMATH DE Number: 6953095
Wikidata QID: Q59130940
describes a project that uses: Sostools
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/3740834
OpenAlex ID: W2336027515
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description: scientific article; zbMATH DE number 6953095