This paper is concerned with the $H_2$ control of linear systems with multiple quantization channels. The quantization parameters of each channel are not required to be identical. The resultant mismatches are represented by polytopic uncertainties. A composite controller composed of linear and nonlinear parts is designed to meet the required $H_2$ performance and offset the quantization error. Resorting to a vertex separation technique and Finsler lemma instead of matrix inverse operations, new synthesis conditions for the desired linear part are derived in terms of linear matrix inequalities, which are further extended to treat systems with norm-bounded uncertainties. A comparison of conservativeness between the proposed methods and the existing ones is demonstrated by two numerical examples.
Bibliographical noteFunding Information:
Manuscript received February 28, 2018; revised June 11, 2018; accepted June 25, 2018. Date of publication July 18, 2018; date of current version March 27, 2019. This work was supported in part by the National Natural Science Foundation of China under Grant 61773200 and Grant 61403189, in part by the peak of six talents in Jiangsu Province under Grant 2015XXRJ-011, in part by the Doctoral Foundation of Ministry of Education of China under Grant 20133221120012, in part by the Natural Science Foundation of Jiangsu Province of China under Grant BK20130949, in part by the National Research Foundation of Korea funded by the Ministry of Science, ICT, and Future Planning under Grant NRF-2017R1A1A1A05001325, and in part by the Brain Korea 21 Plus Project in 2018. Recommended by Associate Editor Serdar Yuksel. (Corresponding author: Choon Ki Ahn.) M. Shen is with the College of Electrical Engineering and Control Science, Nanjing Technology University, Nanjing 211816, China (e-mail: email@example.com).
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- Linear matrix inequalities (LMIs)
- mismatched quantization
- robust control
ASJC Scopus subject areas
- Control and Systems Engineering
- Computer Science Applications
- Electrical and Electronic Engineering