Robust H∞ control for fractional order singular systems 0 < α < 1 with uncertainty
This article studies robust H∞$$ {H}_{\infty } $$ control for fractional order singular systems (FOSS) 0<α<1$$ 0<\alpha <1 $$ with uncertainty. First, the condition based on the linear matrix inequality (LMI) is obtained for fractional order systems with 0<α<1$$ 0<\alpha <1 $...
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| Published in: | Optimal control applications & methods Vol. 44; no. 1; pp. 332 - 348 |
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| ISSN: | 0143-2087, 1099-1514 |
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| Abstract | This article studies robust H∞$$ {H}_{\infty } $$ control for fractional order singular systems (FOSS) 0<α<1$$ 0<\alpha <1 $$ with uncertainty. First, the condition based on the linear matrix inequality (LMI) is obtained for fractional order systems with 0<α<1$$ 0<\alpha <1 $$ in Corollary 1. Compared with existing results, by using two matrices to replace the complex matrix, the condition is easier to solve. Based on Corollary 1, the condition of H∞$$ {H}_{\infty } $$ control based on non‐strict LMI for FOSS without uncertainty is proposed. The strict LMI‐based conditions of H∞$$ {H}_{\infty } $$ control are improved to overcome the equality constraints. Finally, the LMI‐based conditions of robust H∞$$ {H}_{\infty } $$ control are proposed for FOSS. Four examples are shown to illustrate the effectiveness of the method. |
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| AbstractList | This article studies robust control for fractional order singular systems (FOSS) with uncertainty. First, the condition based on the linear matrix inequality (LMI) is obtained for fractional order systems with in Corollary 1. Compared with existing results, by using two matrices to replace the complex matrix, the condition is easier to solve. Based on Corollary 1, the condition of control based on non‐strict LMI for FOSS without uncertainty is proposed. The strict LMI‐based conditions of control are improved to overcome the equality constraints. Finally, the LMI‐based conditions of robust control are proposed for FOSS. Four examples are shown to illustrate the effectiveness of the method. This article studies robust H∞$$ {H}_{\infty } $$ control for fractional order singular systems (FOSS) 0<α<1$$ 0<\alpha <1 $$ with uncertainty. First, the condition based on the linear matrix inequality (LMI) is obtained for fractional order systems with 0<α<1$$ 0<\alpha <1 $$ in Corollary 1. Compared with existing results, by using two matrices to replace the complex matrix, the condition is easier to solve. Based on Corollary 1, the condition of H∞$$ {H}_{\infty } $$ control based on non‐strict LMI for FOSS without uncertainty is proposed. The strict LMI‐based conditions of H∞$$ {H}_{\infty } $$ control are improved to overcome the equality constraints. Finally, the LMI‐based conditions of robust H∞$$ {H}_{\infty } $$ control are proposed for FOSS. Four examples are shown to illustrate the effectiveness of the method. |
| Author | Li, Bingxin Zhao, Xin |
| Author_xml | – sequence: 1 givenname: Bingxin orcidid: 0000-0002-7154-2240 surname: Li fullname: Li, Bingxin organization: Nankai University – sequence: 2 givenname: Xin surname: Zhao fullname: Zhao, Xin email: zhaoxin@nankai.edu.cn organization: Shenzhen Research Institute of Nankai University |
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| Snippet | This article studies robust H∞$$ {H}_{\infty } $$ control for fractional order singular systems (FOSS) 0<α<1$$ 0<\alpha <1 $$ with uncertainty. First, the... This article studies robust control for fractional order singular systems (FOSS) with uncertainty. First, the condition based on the linear matrix inequality... |
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| SubjectTerms | Control systems fractional order singular systems H-infinity control H∞$$ {H}_{\infty } $$ control Linear matrix inequalities linear matrix inequality Mathematical analysis Robust control robust H∞$$ {H}_{\infty } $$ control Uncertainty |
| Title | Robust H∞ control for fractional order singular systems 0 < α < 1 with uncertainty |
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