![](/images/graphics-bg.png)
Construction of a Smooth Lyapunov Function for the Robust and Exact Second-Order Differentiator
Joint Authors
Sanchez, Tonametl
Moreno, Jaime A.
Ortiz-Ricardez, Fernando A.
Source
Mathematical Problems in Engineering
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-04-04
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Sanchez, Tonametl& Moreno, Jaime A.& Ortiz-Ricardez, Fernando A.. 2016. Construction of a Smooth Lyapunov Function for the Robust and Exact Second-Order Differentiator. Mathematical Problems in Engineering،Vol. 2016, no. 2016, pp.1-12.
https://search.emarefa.net/detail/BIM-1112079
Modern Language Association (MLA)
Sanchez, Tonametl…[et al.]. Construction of a Smooth Lyapunov Function for the Robust and Exact Second-Order Differentiator. Mathematical Problems in Engineering No. 2016 (2016), pp.1-12.
https://search.emarefa.net/detail/BIM-1112079
American Medical Association (AMA)
Sanchez, Tonametl& Moreno, Jaime A.& Ortiz-Ricardez, Fernando A.. Construction of a Smooth Lyapunov Function for the Robust and Exact Second-Order Differentiator. Mathematical Problems in Engineering. 2016. Vol. 2016, no. 2016, pp.1-12.
https://search.emarefa.net/detail/BIM-1112079
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1112079