Abstract
This chapter considers the global convergence of Boolean control networks. In the first part, what are effectively the scalar forms of logical variables are used. Hence, the Boolean matrix, which consists of 0 and 1 entries, is discussed first. One of the main tools in this investigation is the vector metric on a set of Boolean matrices. Using this, a sufficient condition for global stability, which means global convergence, is considered. The method is then extended to solving the stabilization of Boolean control systems. In the second part, the algebraic form dynamics are investigated. A necessary and sufficient condition is provided. The primary contents in this chapter are from Cheng et al. (Int. J. Robust Nonlinear Control, 2010).
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References
Cheng, D., Qi, H., Li, Z., Liu, J.B.: Stability and stabilization of Boolean networks. Int. J. Robust Nonlinear Control (2010). doi:10.1002/rnc.1581 (to appear)
Robert, F.: Discrete Iterations: A Metric Study. Springer, Berlin (1986). Translated by J. Rolne
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© 2011 Springer-Verlag London Limited
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Cheng, D., Qi, H., Li, Z. (2011). Stability and Stabilization. In: Analysis and Control of Boolean Networks. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-0-85729-097-7_11
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DOI: https://doi.org/10.1007/978-0-85729-097-7_11
Publisher Name: Springer, London
Print ISBN: 978-0-85729-096-0
Online ISBN: 978-0-85729-097-7
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