Discretized Lyapunov–Krasovskii functional for coupled differential–difference equations with multiple delay channels
Many practical systems have a large number of state variables, but only a few components involve time delays. These components are often scalar or low dimensional, and typically only one delay is present in each such component. A special form of coupled differential–difference equations with one del...
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| Veröffentlicht in: | Automatica (Oxford) Jg. 46; H. 5; S. 902 - 909 |
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| Abstract | Many practical systems have a large number of state variables, but only a few components involve time delays. These components are often scalar or low dimensional, and typically only one delay is present in each such component. A special form of coupled differential–difference equations with one delay per channel proposed recently is well suited to formulate such systems. This article extends the discretized Lyapunov–Krasovskii functional method to this class of systems. In addition to generality, this formulation also drastically reduces the computational cost for a typical system, and therefore is appropriate to use even for time-delay systems of retarded type. The discretized formulation is also simpler than the previous formulation for systems with multiple delays. |
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| AbstractList | Many practical systems have a large number of state variables, but only a few components involve time delays. These components are often scalar or low dimensional, and typically only one delay is present in each such component. A special form of coupled differential-difference equations with one delay per channel proposed recently is well suited to formulate such systems. This article extends the discretized Lyapunov-Krasovskii functional method to this class of systems. In addition to generality, this formulation also drastically reduces the computational cost for a typical system, and therefore is appropriate to use even for time-delay systems of retarded type. The discretized formulation is also simpler than the previous formulation for systems with multiple delays. |
| Author | Gu, Keqin Li, Hongfei |
| Author_xml | – sequence: 1 givenname: Hongfei surname: Li fullname: Li, Hongfei email: lhf8165@163.com organization: Department of Mathematics, Yulin University, Shaanxi Yulin, 719000, China – sequence: 2 givenname: Keqin surname: Gu fullname: Gu, Keqin email: kgu@siue.edu organization: Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL 62026-1805, USA |
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| Cites_doi | 10.1016/0021-8928(65)90029-8 10.1137/0316013 10.1093/imamci/19.1_and_2.157 10.1109/CDC.1982.268218 10.3182/20060710-3-IT-4901.00010 10.1016/0024-3795(94)00183-9 10.3182/20060705-3-FR-2907.00078 10.3182/20020721-6-ES-1901.00191 10.1007/BF01441963 10.1016/0021-8928(64)90073-5 10.1007/BF02412000 10.1109/TAC.2003.815036 10.1080/00207170701383780 10.1080/00207170110047190 10.1016/0022-247X(80)90057-8 10.1016/S0022-247X(02)00202-0 10.1002/rnc.750 10.1016/j.automatica.2010.01.028 10.1115/DSCC2008-2282 10.1016/S0005-1098(02)00195-4 10.1016/j.automatica.2008.10.024 10.1016/j.automatica.2009.03.019 10.1137/0503042 10.1137/0307044 10.1090/qam/99914 10.1109/CDC.2006.376937 10.1016/0022-0396(70)90114-2 10.1016/0362-546X(78)90048-2 10.1109/ICEEE.2005.1529641 10.1109/TAC.1971.1099834 10.1016/0022-247X(70)90283-0 |
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| Keywords | Lyapunov–Krasovskii functional Delay Coupled differential–difference equations Differential equation Differential form Coupled differential-difference equations Lyapunov method Multiple delay Delay system Difference equation Delay equation Occupation time Delay time Lyapunov―Krasovskii functional Multiple channel Lyapunov function |
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| SubjectTerms | Applied sciences Channels Computational efficiency Computer science; control theory; systems Control system analysis Control theory. Systems Coupled differential–difference equations Delay Exact sciences and technology Formulations Lyapunov–Krasovskii functional Mathematical analysis Mathematical models Scalars Time delay |
| Title | Discretized Lyapunov–Krasovskii functional for coupled differential–difference equations with multiple delay channels |
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