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Abstract
This article is concerned with the observability and accessibility of discrete impulsive nonlinear systems. A geometric method based on the differential geometric analysis and Lie group investigation is proposed. The infinitesimal invariance principle in Lie group theory is extended to the case of discrete impulsive nonlinear systems. By characterising the infinitesimal principle in terms of the sequences of codistribution and distribution, explicit criteria for the local observability and local accessibility of the system are derived, respectively. Additionally, two examples are provided to show that the criteria are convenient to check.
Acknowledgements
The authors would like to thank the editor and the reviewers for their constructive comments and suggestions to improve the quality of this article. This work was supported by the NNSF of China under Grant 60874027 and 60114039, the Fundamental Research Funds for the Central Universities of China, and Shanghai Municipal Education Commission Research Funding (No. gjd10009, No. A-3500-11-10).