Abstract
This chapter introduces a new concept: the input-state incidence matrix (ISIM) of a Boolean control network. This provides an algebraic description of the geometric structure of the control network in the input-state product space. As a row-periodic matrix, the structure of the ISIM is explored in detail. Then we show its applications to investigating the controllability, observability, and the topological structure of the input-state transfer graph. Finally, the same problems are discussed for mix-valued logical dynamic systems. This chapter is based on Zhao et al. (Syst. Control Lett., 2010).
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References
Li, Z., Cheng, D.: Algebraic approach to dynamics of multi-valued networks. Int. J. Bifurc. Chaos 20(3), 561–582 (2010)
Mu, Y., Guo, L.: Optimization and identification in a non-equilibrium dynamic game. In: Proc. CDC-CCC’09, pp. 5750–5755 (2009)
Zhao, Y., Qi, H., Cheng, D.: Input-state incidence matrix of Boolean control networks and its applications. Syst. Control Lett. (2010). doi:10.1016/j.sysconle.2010.09.002
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© 2011 Springer-Verlag London Limited
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Cheng, D., Qi, H., Li, Z. (2011). Input-State Incidence Matrices. In: Analysis and Control of Boolean Networks. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-0-85729-097-7_16
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DOI: https://doi.org/10.1007/978-0-85729-097-7_16
Publisher Name: Springer, London
Print ISBN: 978-0-85729-096-0
Online ISBN: 978-0-85729-097-7
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