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Strong 𝐗 -robustness of interval max-min matrices

Helena Myšková, Ján Plavka (2021)

Kybernetika

In max-min algebra the standard pair of operations plus and times is replaced by the pair of operations maximum and minimum, respectively. A max-min matrix A is called strongly robust if the orbit x , A x , A 2 x , reaches the greatest eigenvector with any starting vector. We study a special type of the strong robustness called the strong X-robustness, the case that a starting vector is limited by a lower bound vector and an upper bound vector. The equivalent condition for the strong X-robustness is introduced...

Systems with associative dynamics

Ronald Korin Pearson, Ülle Kotta, Sven Nōmm (2002)

Kybernetika

This paper introduces a class of nonlinear discrete-time dynamic models that generalize familiar linear model structures; our motivation is to explore the extent to which known results for the linear case do or do not extend to this nonlinear class. The results presented here are based on a complete characterization of the solution of the associative functional equation F [ F ( x , y ) , z ] = F [ x , F ( y , z ) ] due to J. Aczel, leading to a class of invertible binary operators that includes addition, multiplication, and infinitely many...

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