Title: Analysis of mix-valued logical control networks

Authors: Zhiqiang Li; Huimin Xiao; Jinli Song

Addresses: Department of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou, China ' Department of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou, China ' Department of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou, China

Abstract: Using semi-tensor product and the vector form of multi-valued logical variables, the mix-valued logical system is expressed as a linear discrete time system and the mix-valued logical control system is expressed as a bilinear discrete time system with respect to the state and control variables. In this paper, the topological property of mix-valued logical network and the reachability and controllability of mix-valued logical control systems are discussed. From the algebraic form of mix-valued logical network, we obtain the number of the logical system. The formula we obtained is based on the rank of structure matrix. Also, the necessary and sufficient conditions are obtained for testing the reachability and controllability.

Keywords: semi-tensor products; STP; mix-valued logical networks; reachability; controllability; linear discrete time; bilinear discrete time; state variables; control variables; mix-valued logical control.

DOI: 10.1504/IJAMECHS.2013.060018

International Journal of Advanced Mechatronic Systems, 2013 Vol.5 No.6, pp.401 - 409

Published online: 19 Mar 2014 *

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