Invariance Pressure Dimensions for Control Systems
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We introduce two kinds of invariance pressure dimension, which not only give dimension characteristics of invariance pressure and inner invariance pressure introduced by Colonius et al. (J Dyn Differ Equ, https://doi.org/10.1007/s10884-018-9646-2, 2018) for discrete-time control systems, but also generalize the corresponding concepts proposed by Huang and Zhong (Syst Control Lett 112:36–41, 2018). Then we derive some basic properties for them and investigate the relations among these invariance pressures defined by controls and by invariant covers. As an application, we characterize the complexity of a control system with zero invariance entropy.
KeywordsControl system Invariance pressure Dimension characteristic Zero invariance entropy
The authors are grateful to the referees for their valuable comments which have led to improvement of the paper. A part of this work was done when the first author visited Western University. The author would like to thank Prof. X. Zou and his institute for their hospitality.
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