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Construction of a Smooth Lyapunov Function for the Robust and Exact Second-Order Differentiator
- Source :
- Mathematical Problems in Engineering, Vol 2016 (2016)
- Publication Year :
- 2016
- Publisher :
- Hindawi Limited, 2016.
-
Abstract
- 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.
- Subjects :
- Lyapunov function
0209 industrial biotechnology
Article Subject
lcsh:Mathematics
General Mathematics
General Engineering
Lyapunov optimization
02 engineering and technology
Lyapunov exponent
lcsh:QA1-939
Differentiator
symbols.namesake
020901 industrial engineering & automation
Positive definiteness
lcsh:TA1-2040
Control theory
0202 electrical engineering, electronic engineering, information engineering
symbols
020201 artificial intelligence & image processing
Lyapunov equation
lcsh:Engineering (General). Civil engineering (General)
Lyapunov redesign
Control-Lyapunov function
Mathematics
Subjects
Details
- ISSN :
- 15635147 and 1024123X
- Volume :
- 2016
- Database :
- OpenAIRE
- Journal :
- Mathematical Problems in Engineering
- Accession number :
- edsair.doi.dedup.....8434330ac49cb8c10bba9648658cf240