2007 Fiscal Year Final Research Report Summary
Analysis and Control of Synchronization in Coupled Nonlinear Systems with Time-delays
| Project/Area Number |
18560441
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Control engineering
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| Research Institution | Tokyo Metropolitan University |
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Principal Investigator |
OGUCHI Toshiki Tokyo Metropolitan University, Graduate School of Science and Engineering, Associate Professor (50295474)
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| Project Period (FY) |
2006 – 2007
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| Keywords | Control Engineering / Time-delays / Nonlinear systems / Synchronization / Chaotic systems |
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| Research Abstract |
This project has been carried out in two phases.
(a) The first phase was to study on synchronization of two coupled nonlinear systems with time-varying delay. In this phase, we introduced the notion of strict semi-dissipativity and showed the convergence property of coupled systems that each system satisfies the strict semi-passive by using the small gain theorem. By using this result, the bounds of the trajectories can be estimated and then a sufficient condition for synchronization can be derived in the form of Linear Matrix Inequalities (LMIs). In addition, in this phase, we proposed a new configuration of anticipating synchronization with the state observer.
(b) The second phase was to extend the results in the first phase into N coupled systems. First, we derived a necessary condition under which the synchronization error dynamics has the origin as an equilibrium solution. The obtained condition means that the networks must have symmetric structures. Under the condition, we obtained sufficient conditions for synchronization in unidirectional or bidirectional networks of N chaotic systems with time-delay coupling. The synchronization conditions derived in this project are based on the Lyapunov-Krasovskii theorem in combination with the LyapunoVs indirect method. The obtained conditions were verified by numerical simulations.
In this paper we targeted on only complete synchronization of coupled systems and have uncovered a phenomenon of partial synchronization in networks. Therefore the analysis of partial synchronization will be the subject of further research.
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