Absolute Stability Criteria for Large-Scale Lurie Direct Control Systems with Time-Varying Coefficients
The absolute stability of large-scale Lurie direct control systems with time-varying coefficients is investigated. Based on the decomposition method for large-scale systems and technique of the nonsingular M-matrix, a suitable scalar Lyapunov function as a weighted sum is constructed. By estimating...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/631604 |
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| author | Fucheng Liao Di Wang |
| author_facet | Fucheng Liao Di Wang |
| author_sort | Fucheng Liao |
| collection | DOAJ |
| description | The absolute stability of large-scale Lurie direct control systems with time-varying coefficients is investigated. Based on the decomposition method for large-scale systems and technique of the nonsingular M-matrix, a suitable scalar Lyapunov function as a weighted sum is constructed. By estimating its total time derivative, some absolute stability criteria and practical corollaries are derived. Furthermore, the results are extended to multiple nonlinearities. The salient feature of this paper is that the criteria which we propose allow for the situation that the norms of time-varying coefficients are unbounded. The main idea of the methodology is that even if the coefficients are norm-unbounded, by restricting their relative magnitude, the problem of negative definiteness for the derivative can also be changed into the problem of stability for a constant matrix. Finally, some numerical examples are included to illustrate the effectiveness of the proposed criteria. |
| format | Article |
| id | doaj-art-794348d1e8b14ce08a37e8076ebfca2d |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-794348d1e8b14ce08a37e8076ebfca2d2025-08-20T03:35:23ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/631604631604Absolute Stability Criteria for Large-Scale Lurie Direct Control Systems with Time-Varying CoefficientsFucheng Liao0Di Wang1School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, ChinaSchool of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, ChinaThe absolute stability of large-scale Lurie direct control systems with time-varying coefficients is investigated. Based on the decomposition method for large-scale systems and technique of the nonsingular M-matrix, a suitable scalar Lyapunov function as a weighted sum is constructed. By estimating its total time derivative, some absolute stability criteria and practical corollaries are derived. Furthermore, the results are extended to multiple nonlinearities. The salient feature of this paper is that the criteria which we propose allow for the situation that the norms of time-varying coefficients are unbounded. The main idea of the methodology is that even if the coefficients are norm-unbounded, by restricting their relative magnitude, the problem of negative definiteness for the derivative can also be changed into the problem of stability for a constant matrix. Finally, some numerical examples are included to illustrate the effectiveness of the proposed criteria.http://dx.doi.org/10.1155/2014/631604 |
| spellingShingle | Fucheng Liao Di Wang Absolute Stability Criteria for Large-Scale Lurie Direct Control Systems with Time-Varying Coefficients The Scientific World Journal |
| title | Absolute Stability Criteria for Large-Scale Lurie Direct Control Systems with Time-Varying Coefficients |
| title_full | Absolute Stability Criteria for Large-Scale Lurie Direct Control Systems with Time-Varying Coefficients |
| title_fullStr | Absolute Stability Criteria for Large-Scale Lurie Direct Control Systems with Time-Varying Coefficients |
| title_full_unstemmed | Absolute Stability Criteria for Large-Scale Lurie Direct Control Systems with Time-Varying Coefficients |
| title_short | Absolute Stability Criteria for Large-Scale Lurie Direct Control Systems with Time-Varying Coefficients |
| title_sort | absolute stability criteria for large scale lurie direct control systems with time varying coefficients |
| url | http://dx.doi.org/10.1155/2014/631604 |
| work_keys_str_mv | AT fuchengliao absolutestabilitycriteriaforlargescaleluriedirectcontrolsystemswithtimevaryingcoefficients AT diwang absolutestabilitycriteriaforlargescaleluriedirectcontrolsystemswithtimevaryingcoefficients |