Back to Search
Start Over
Stabilization of a one-dimensional wave equation with variable coefficient under non-collocated control and delayed observation
- Source :
- Mathematical Methods in the Applied Sciences.
- Publication Year :
- 2017
- Publisher :
- Wiley, 2017.
-
Abstract
- In this paper, we consider stabilization of a 1-dimensional wave equation with variable coefficient where non-collocated boundary observation suffers from an arbitrary time delay. Since input and output are non-collocated with each other, it is more complex to design the observer system. After showing well-posedness of the open-loop system, the observer and predictor systems are constructed to give the estimated state feedback controller. Different from the partial differential equation with constant coefficients, the variable coefficient causes mathematical difficulties of the stabilization problem. By the approach of Riesz basis property, it is shown that the closed-loop system is stable exponentially. Numerical simulations demonstrate the effect of the stable controller. This paper is devoted to the wave equation with variable coefficients generalized of that with constant coefficients for delayed observation and non-collocated control.
- Subjects :
- 0209 industrial biotechnology
Constant coefficients
Partial differential equation
Observer (quantum physics)
General Mathematics
010102 general mathematics
Mathematical analysis
General Engineering
Characteristic equation
02 engineering and technology
Wave equation
01 natural sciences
020901 industrial engineering & automation
Exponential stability
Control theory
Full state feedback
0101 mathematics
Mathematics
Variable (mathematics)
Subjects
Details
- ISSN :
- 01704214
- Database :
- OpenAIRE
- Journal :
- Mathematical Methods in the Applied Sciences
- Accession number :
- edsair.doi...........0c2b35c2f4c478a092ffe6158b56970c