Alternate Admissibility LMI Criteria for Descriptor Fractional Order Systems with 0 < <i>α</i> < 2
The paper focuses on the admissibility problem of descriptor fractional-order systems (DFOSs). The alternate admissibility criteria are addressed for DFOSs with order in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics>...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-07-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/7/8/577 |
| _version_ | 1797584735796461568 |
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| author | Ying Di Jin-Xi Zhang Xuefeng Zhang |
| author_facet | Ying Di Jin-Xi Zhang Xuefeng Zhang |
| author_sort | Ying Di |
| collection | DOAJ |
| description | The paper focuses on the admissibility problem of descriptor fractional-order systems (DFOSs). The alternate admissibility criteria are addressed for DFOSs with order in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></semantics></math></inline-formula> which involve a non-strict linear matrix inequality (LMI) method and a strict LMI method, respectively. The forms of non-strict and strict LMIs are brand new and distinguished with the existing literature, which fills the gaps of studies for admissibility. These necessary and sufficient conditions of admissibility are available to the order in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></semantics></math></inline-formula> without separating the order ranges into <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>[</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></semantics></math></inline-formula>. Based on the special position of singular matrix, the non-strict LMI criterion has an advantage in handling the DFOSs with uncertain derivative matrices. For the strict LMI form, a method involving least real decision variables is derived which is more convenient to process the practical solution. Three numerical examples are given to illustrate the validity of the proposed results. |
| first_indexed | 2024-03-10T23:55:51Z |
| format | Article |
| id | doaj.art-fbbc26b5aade4f2baaf47a23f6907cd7 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T23:55:51Z |
| publishDate | 2023-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-fbbc26b5aade4f2baaf47a23f6907cd72023-11-19T01:10:52ZengMDPI AGFractal and Fractional2504-31102023-07-017857710.3390/fractalfract7080577Alternate Admissibility LMI Criteria for Descriptor Fractional Order Systems with 0 < <i>α</i> < 2Ying Di0Jin-Xi Zhang1Xuefeng Zhang2College of Sciences, Northeastern University, Shenyang 110819, ChinaState Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110819, ChinaCollege of Sciences, Northeastern University, Shenyang 110819, ChinaThe paper focuses on the admissibility problem of descriptor fractional-order systems (DFOSs). The alternate admissibility criteria are addressed for DFOSs with order in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></semantics></math></inline-formula> which involve a non-strict linear matrix inequality (LMI) method and a strict LMI method, respectively. The forms of non-strict and strict LMIs are brand new and distinguished with the existing literature, which fills the gaps of studies for admissibility. These necessary and sufficient conditions of admissibility are available to the order in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></semantics></math></inline-formula> without separating the order ranges into <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>[</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></semantics></math></inline-formula>. Based on the special position of singular matrix, the non-strict LMI criterion has an advantage in handling the DFOSs with uncertain derivative matrices. For the strict LMI form, a method involving least real decision variables is derived which is more convenient to process the practical solution. Three numerical examples are given to illustrate the validity of the proposed results.https://www.mdpi.com/2504-3110/7/8/577descriptor fractional order systemsadmissibilityunified criterionlinear matrix inequality |
| spellingShingle | Ying Di Jin-Xi Zhang Xuefeng Zhang Alternate Admissibility LMI Criteria for Descriptor Fractional Order Systems with 0 < <i>α</i> < 2 Fractal and Fractional descriptor fractional order systems admissibility unified criterion linear matrix inequality |
| title | Alternate Admissibility LMI Criteria for Descriptor Fractional Order Systems with 0 < <i>α</i> < 2 |
| title_full | Alternate Admissibility LMI Criteria for Descriptor Fractional Order Systems with 0 < <i>α</i> < 2 |
| title_fullStr | Alternate Admissibility LMI Criteria for Descriptor Fractional Order Systems with 0 < <i>α</i> < 2 |
| title_full_unstemmed | Alternate Admissibility LMI Criteria for Descriptor Fractional Order Systems with 0 < <i>α</i> < 2 |
| title_short | Alternate Admissibility LMI Criteria for Descriptor Fractional Order Systems with 0 < <i>α</i> < 2 |
| title_sort | alternate admissibility lmi criteria for descriptor fractional order systems with 0 i α i 2 |
| topic | descriptor fractional order systems admissibility unified criterion linear matrix inequality |
| url | https://www.mdpi.com/2504-3110/7/8/577 |
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