<inline-formula> <tex-math notation="LaTeX">$\ell_\infty$ </tex-math></inline-formula>-Gain Analysis of Discrete-Time Positive Singular Systems With Time-Varying Delays
This paper is concerned with the ℓ<sub>∞</sub>-gain analysis problem of discrete-time positive singular systems with time-varying delays. By introducing an auxiliary system, a necessary and sufficient positivity condition is proposed for systems. Then, by using of t...
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/8853250/ |
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doaj-663ff791d331480e9f15c4e6d1cb40ff2021-04-05T17:34:52ZengIEEEIEEE Access2169-35362019-01-01714312014312610.1109/ACCESS.2019.29446338853250<inline-formula> <tex-math notation="LaTeX">$\ell_\infty$ </tex-math></inline-formula>-Gain Analysis of Discrete-Time Positive Singular Systems With Time-Varying DelaysYukang Cui0https://orcid.org/0000-0001-8783-7441Hao Feng1Guang-Zhong Cao2School of Three Gorges Artificial Intelligence, Chongqing Three Gorges University, Chongqing, ChinaShenzhen Key Laboratory of Electromagnetic Control, College of Mechatronics and Control Engineering, Shenzhen University, Shenzhen, ChinaShenzhen Key Laboratory of Electromagnetic Control, College of Mechatronics and Control Engineering, Shenzhen University, Shenzhen, ChinaThis paper is concerned with the ℓ<sub>∞</sub>-gain analysis problem of discrete-time positive singular systems with time-varying delays. By introducing an auxiliary system, a necessary and sufficient positivity condition is proposed for systems. Then, by using of the positivity and linearity, we investigate the monotonic and asymptotic property of the system with time-varying delays. Then, by resorting to the comparing system with constant delays, an explicit expression of the ℓ<sub>∞</sub>-gain of discrete-time singular systems with time-varying delays is given in terms of system matrices. The result shows that ℓ<sub>∞</sub>-gain of discrete-time positive singular systems with bounded time-varying delays is insensitive to the magnitude of delays.https://ieeexplore.ieee.org/document/8853250/Positive systemssingular systemstime-delay<italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">ℓ</italic>∞-gain |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Yukang Cui Hao Feng Guang-Zhong Cao |
| spellingShingle |
Yukang Cui Hao Feng Guang-Zhong Cao <inline-formula> <tex-math notation="LaTeX">$\ell_\infty$ </tex-math></inline-formula>-Gain Analysis of Discrete-Time Positive Singular Systems With Time-Varying Delays IEEE Access Positive systems singular systems time-delay <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">ℓ</italic>∞-gain |
| author_facet |
Yukang Cui Hao Feng Guang-Zhong Cao |
| author_sort |
Yukang Cui |
| title |
<inline-formula> <tex-math notation="LaTeX">$\ell_\infty$ </tex-math></inline-formula>-Gain Analysis of Discrete-Time Positive Singular Systems With Time-Varying Delays |
| title_short |
<inline-formula> <tex-math notation="LaTeX">$\ell_\infty$ </tex-math></inline-formula>-Gain Analysis of Discrete-Time Positive Singular Systems With Time-Varying Delays |
| title_full |
<inline-formula> <tex-math notation="LaTeX">$\ell_\infty$ </tex-math></inline-formula>-Gain Analysis of Discrete-Time Positive Singular Systems With Time-Varying Delays |
| title_fullStr |
<inline-formula> <tex-math notation="LaTeX">$\ell_\infty$ </tex-math></inline-formula>-Gain Analysis of Discrete-Time Positive Singular Systems With Time-Varying Delays |
| title_full_unstemmed |
<inline-formula> <tex-math notation="LaTeX">$\ell_\infty$ </tex-math></inline-formula>-Gain Analysis of Discrete-Time Positive Singular Systems With Time-Varying Delays |
| title_sort |
<inline-formula> <tex-math notation="latex">$\ell_\infty$ </tex-math></inline-formula>-gain analysis of discrete-time positive singular systems with time-varying delays |
| publisher |
IEEE |
| series |
IEEE Access |
| issn |
2169-3536 |
| publishDate |
2019-01-01 |
| description |
This paper is concerned with the ℓ<sub>∞</sub>-gain analysis problem of discrete-time positive singular systems with time-varying delays. By introducing an auxiliary system, a necessary and sufficient positivity condition is proposed for systems. Then, by using of the positivity and linearity, we investigate the monotonic and asymptotic property of the system with time-varying delays. Then, by resorting to the comparing system with constant delays, an explicit expression of the ℓ<sub>∞</sub>-gain of discrete-time singular systems with time-varying delays is given in terms of system matrices. The result shows that ℓ<sub>∞</sub>-gain of discrete-time positive singular systems with bounded time-varying delays is insensitive to the magnitude of delays. |
| topic |
Positive systems singular systems time-delay <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">ℓ</italic>∞-gain |
| url |
https://ieeexplore.ieee.org/document/8853250/ |
| work_keys_str_mv |
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| _version_ |
1721539294886100992 |