Special decentralized control problems in discrete-time interconnected systems composed of two subsystems |
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Authors: | Zhisheng Duan Jinzhi Wang Lin Huang |
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Affiliation: | aState Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Engineering Science, Peking University, Beijing 100871, PR China |
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Abstract: | In this paper, some special decentralized control problems are addressed for discrete-time interconnected systems. First it is pointed out that some subsystems must be unstable to ensure stability of the overall system in some special cases. Then a special kind of decentralized control problem is studied. This kind of problem can be viewed as harmonic control among independent subsystems. Research results show that two unstable systems can generate a stable system through some effective cooperations. In addition, a decentralized controller design method based on linear matrix inequality is also given by using parameter-dependent Lyapunov function method developed for the study of robust stability. A special linear star coupled dynamical network is also considered. The central subsystem must be unstable to stabilize the whole network under a special coupling. Several examples are given to illustrate the results. |
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Keywords: | Interconnected systems Decentralized control Parameter-dependent Lyapunov function (PDLF) Linear matrix inequality (LMI) Star coupled network |
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