<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Design of a state observer is an important issue in control systems and signal processing. It is well known that it is difficult to obtain the desired properties of state feedback control if some or all of the system states cannot be directly measured. Moreover, the existence of a lumped perturbation and/or a time delay usually reduces the system performance or even produces an instability in the closed-loop system. Therefore, in this paper, a new Variable Structure Observer (VSO) is proposed for a class of uncertain systems subjected to a time varying delay and a lumped perturbation. Based on the strictly positive real concept, the stability of the equivalent error system is verified. Based on the generalized matrix inverse approach, the global reaching condition of the sliding mode of the error system is guaranteed. Also, the proposed variable structure observer will be shown to possess the invariance property in relation to the lumped perturbation, as the traditional variable structure controller does. Furthermore, two illustrative examples with a series of computer simulation studies are given to demonstrate the effectiveness of the proposed design method.</p></abstract>

Design of a state observer is an important issue in control systems and signal processing. It is well known that it is difficult to obtain the desired properties of state feedback control if some or all of the system states cannot be directly measured. Moreover, the existence of a lumped perturbation and/or a time delay usually reduces the system performance or even produces an instability in the closed-loop system. Therefore, in this paper, a new Variable Structure Observer (VSO) is proposed for a class of uncertain systems subjected to a time varying delay and a lumped perturbation. Based on the strictly positive real concept, the stability of the equivalent error system is verified. Based on the generalized matrix inverse approach, the global reaching condition of the sliding mode of the error system is guaranteed. Also, the proposed variable structure observer will be shown to possess the invariance property in relation to the lumped perturbation, as the traditional variable structure controller does. Furthermore, two illustrative examples with a series of computer simulation studies are given to demonstrate the effectiveness of the proposed design method.

Variable structure observer design for a class of uncertain systems with a time-varying delay

Department of Electronic Engineering Nan-Kai University of Technology, Tsao-tun 542, Nan-Tou, Taiwan, ROC

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Design of a state observer is an important issue in control systems and signal processing. It is well known that it is difficult to obtain the desired...

Variable structure observer design for a class of uncertain systems with a time-varying delay

Published Online: Sep 28, 2012

Page range: 575 - 583

DOI: https://doi.org/10.2478/v10006-012-0044-3

Keywords
variable structure observer, invariance property, generalized matrix inverse approach

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Variable structure observer design for a class of uncertain systems with a time-varying delay

Published Online: Sep 28, 2012

Page range: 575 - 583

DOI: https://doi.org/10.2478/v10006-012-0044-3

Keywordsvariable structure observer, invariance property, generalized matrix inverse approach

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
variable structure observer, invariance property, generalized matrix inverse approach