Contraction Mapping Theory and Approach to LMI-Based Stability Criteria of T-S Fuzzy Impulsive Time-Delays Integrodifferential Equations
In this paper, Banach fixed point theorem is employed to derive LMI-based exponential stability of impulsive Takagi-Sugeno (T-S) fuzzy integrodifferential equations, originated from Cohen-Grossberg Neural Networks (CGNNs). As far as we know, Banach fixed point theorem is rarely employed to derive LM...
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2016-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2016/5035618 |
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| author | Ruofeng Rao Shouming Zhong |
| author_facet | Ruofeng Rao Shouming Zhong |
| author_sort | Ruofeng Rao |
| collection | DOAJ |
| description | In this paper, Banach fixed point theorem is employed to derive LMI-based exponential stability of impulsive Takagi-Sugeno (T-S) fuzzy integrodifferential equations, originated from Cohen-Grossberg Neural Networks (CGNNs). As far as we know, Banach fixed point theorem is rarely employed to derive LMI criteria for T-S fuzzy CGNNs, and this inspires our present work. It is worth mentioning that the conditions on the behavior functions are weaker than those of existing results, and the formulated contraction mapping and fixed point technique are different from those of previous literature. Even a corollary of our main result improves one of existing main results due to extending linear function to nonlinear function. Besides, the LMI-based criteria are programmable for computer MATLAB LMI toolbox. Moreover, an analytical table and a numerical example are presented to illustrate the advantage, feasibility, and effectiveness of the proposed methods. |
| format | Article |
| id | doaj-art-9706f6f57dbe4fd2b04bdcb870933bea |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-9706f6f57dbe4fd2b04bdcb870933bea2025-02-03T05:53:58ZengWileyJournal of Function Spaces2314-88962314-88882016-01-01201610.1155/2016/50356185035618Contraction Mapping Theory and Approach to LMI-Based Stability Criteria of T-S Fuzzy Impulsive Time-Delays Integrodifferential EquationsRuofeng Rao0Shouming Zhong1Department of Mathematics, Chengdu Normal University, Chengdu 61130, ChinaResearch Institute of Mathematics, Chengdu Normal University, Chengdu 61130, ChinaIn this paper, Banach fixed point theorem is employed to derive LMI-based exponential stability of impulsive Takagi-Sugeno (T-S) fuzzy integrodifferential equations, originated from Cohen-Grossberg Neural Networks (CGNNs). As far as we know, Banach fixed point theorem is rarely employed to derive LMI criteria for T-S fuzzy CGNNs, and this inspires our present work. It is worth mentioning that the conditions on the behavior functions are weaker than those of existing results, and the formulated contraction mapping and fixed point technique are different from those of previous literature. Even a corollary of our main result improves one of existing main results due to extending linear function to nonlinear function. Besides, the LMI-based criteria are programmable for computer MATLAB LMI toolbox. Moreover, an analytical table and a numerical example are presented to illustrate the advantage, feasibility, and effectiveness of the proposed methods.http://dx.doi.org/10.1155/2016/5035618 |
| spellingShingle | Ruofeng Rao Shouming Zhong Contraction Mapping Theory and Approach to LMI-Based Stability Criteria of T-S Fuzzy Impulsive Time-Delays Integrodifferential Equations Journal of Function Spaces |
| title | Contraction Mapping Theory and Approach to LMI-Based Stability Criteria of T-S Fuzzy Impulsive Time-Delays Integrodifferential Equations |
| title_full | Contraction Mapping Theory and Approach to LMI-Based Stability Criteria of T-S Fuzzy Impulsive Time-Delays Integrodifferential Equations |
| title_fullStr | Contraction Mapping Theory and Approach to LMI-Based Stability Criteria of T-S Fuzzy Impulsive Time-Delays Integrodifferential Equations |
| title_full_unstemmed | Contraction Mapping Theory and Approach to LMI-Based Stability Criteria of T-S Fuzzy Impulsive Time-Delays Integrodifferential Equations |
| title_short | Contraction Mapping Theory and Approach to LMI-Based Stability Criteria of T-S Fuzzy Impulsive Time-Delays Integrodifferential Equations |
| title_sort | contraction mapping theory and approach to lmi based stability criteria of t s fuzzy impulsive time delays integrodifferential equations |
| url | http://dx.doi.org/10.1155/2016/5035618 |
| work_keys_str_mv | AT ruofengrao contractionmappingtheoryandapproachtolmibasedstabilitycriteriaoftsfuzzyimpulsivetimedelaysintegrodifferentialequations AT shoumingzhong contractionmappingtheoryandapproachtolmibasedstabilitycriteriaoftsfuzzyimpulsivetimedelaysintegrodifferentialequations |