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An Introduction to Stability Analysis of Linguistic Fuzzy Dynamic Systems
Published in Seyed Kamaleddin Yadavar Nikravesh, Nonlinear Systems Stability Analysis, 2018
Seyed Kamaleddin Yadavar Nikravesh
A Boolean matrix is defined as a matrix with the same size as the relational matrix with only zero and one as its elements such that each element is zero (one) when the corresponding element in the relational matrix is zero (nonzero). The transformation that maps a relational matrix to its Boolean matrix is called Boolean mapping and is denoted with B(R), where the relational matrix is.
Model matching of switched asynchronous sequential machines via matrix approach
Published in International Journal of Control, 2019
Biao Wang, Jun-e Feng, Min Meng
Consider a single input/state ASM Σi = {Δm, Δn, δln, Fi} without connecting to other ASMs. If an input character δjm is received, the next stable state of Σi is . Thus, records all 1 step stably reachable states of Σi. Hence, we could use an n × n matrix Mi to describe stable reachability of Σi, in which Mi(p, q) = 1 means that xp is stably reachable from xq. We call Mi the stabletransitionmatrix of Σi. Obviously, Mi is a Boolean matrix.
A graph theory approach for regional controllability of Boolean cellular automata
Published in International Journal of Parallel, Emergent and Distributed Systems, 2020
S. Dridi, S. El Yacoubi, F. Bagnoli, A. Fontaine
We denote by the transition matrix which is the associate adjacency matrix of the graph ϒ. The transition matrix is built as a Boolean matrix of size . There is a 1 at position , the row and column, if there is an arc between vertices i and j for all i,j in . Otherwise it stays at 0.
Off-line fault detection of logical control networks
Published in International Journal of Systems Science, 2022
Wenhui Dou, Guodong Zhao, Haitao Li, Qi Chen
is the set of integers. is the set of the -dimensional real matrices. . , where represents the k-dimensional identity matrix and is called the vector form of the logical value . . denotes the th entry of matrix and denotes the ith column of M. Consider the -dimensional matrix L. For any , if there exists a unique k such that , ( and ), then L is called the logical matrix. is the set of the -dimensional logical matrices. Consider the -dimensional matrix B. If , then B is called the Boolean matrix. is the set of the -dimensional Boolean matrices. .