Volume 7, Issue 2
Output Feedback Admissible Control for Singular Systems: Delta Operator (Discretised) Approach

Xin-Zhuang Dong & Mingqing Xiao

East Asian J. Appl. Math., 7 (2017), pp. 248-268.

Published online: 2018-02

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  • Abstract

Singular systems simultaneously capture the dynamics and algebraic constraints in many practical applications. Output feedback admissible control for singular systems through a delta operator method is considered in this article. Two novel admissibility conditions, derived for the singular delta operator system (SDOS) from a singular continuous system through sampling, can not only produce unified admissibility for both continuous and discrete singular systems but also practical procedures. To solve the problem of output feedback admissible control for the SDOS, an existence condition and design procedure is given for the determination of a physically realisable observer for the state estimation, and then a suitable state-feedback-like admissible controller design based on the observer is developed. All of the conditions presented are necessary and sufficient, involving strict linear matrix inequalities (LMI) with feasible solutions obtained with low computational costs. Numerical examples illustrate our approach.

  • Keywords

Singular delta operator system (SDOS), admissibility, output feedback, state observer, linear matrix inequalities (LMI).

  • AMS Subject Headings

93B07, 93B51, 93B52

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-7-248, author = {Xin-Zhuang and Dong and and 17968 and and Xin-Zhuang Dong and Mingqing and Xiao and and 17969 and and Mingqing Xiao}, title = {Output Feedback Admissible Control for Singular Systems: Delta Operator (Discretised) Approach}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {7}, number = {2}, pages = {248--268}, abstract = {

Singular systems simultaneously capture the dynamics and algebraic constraints in many practical applications. Output feedback admissible control for singular systems through a delta operator method is considered in this article. Two novel admissibility conditions, derived for the singular delta operator system (SDOS) from a singular continuous system through sampling, can not only produce unified admissibility for both continuous and discrete singular systems but also practical procedures. To solve the problem of output feedback admissible control for the SDOS, an existence condition and design procedure is given for the determination of a physically realisable observer for the state estimation, and then a suitable state-feedback-like admissible controller design based on the observer is developed. All of the conditions presented are necessary and sufficient, involving strict linear matrix inequalities (LMI) with feasible solutions obtained with low computational costs. Numerical examples illustrate our approach.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.250216.161016a}, url = {http://global-sci.org/intro/article_detail/eajam/10748.html} }
TY - JOUR T1 - Output Feedback Admissible Control for Singular Systems: Delta Operator (Discretised) Approach AU - Dong , Xin-Zhuang AU - Xiao , Mingqing JO - East Asian Journal on Applied Mathematics VL - 2 SP - 248 EP - 268 PY - 2018 DA - 2018/02 SN - 7 DO - http://doi.org/10.4208/eajam.250216.161016a UR - https://global-sci.org/intro/article_detail/eajam/10748.html KW - Singular delta operator system (SDOS), admissibility, output feedback, state observer, linear matrix inequalities (LMI). AB -

Singular systems simultaneously capture the dynamics and algebraic constraints in many practical applications. Output feedback admissible control for singular systems through a delta operator method is considered in this article. Two novel admissibility conditions, derived for the singular delta operator system (SDOS) from a singular continuous system through sampling, can not only produce unified admissibility for both continuous and discrete singular systems but also practical procedures. To solve the problem of output feedback admissible control for the SDOS, an existence condition and design procedure is given for the determination of a physically realisable observer for the state estimation, and then a suitable state-feedback-like admissible controller design based on the observer is developed. All of the conditions presented are necessary and sufficient, involving strict linear matrix inequalities (LMI) with feasible solutions obtained with low computational costs. Numerical examples illustrate our approach.

Xin-Zhuang Dong & MingqingXiao. (2020). Output Feedback Admissible Control for Singular Systems: Delta Operator (Discretised) Approach. East Asian Journal on Applied Mathematics. 7 (2). 248-268. doi:10.4208/eajam.250216.161016a
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