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Rational realization of the minimum ranks of nonnegative sign pattern matrices

Wei Fang, Wei Gao, Yubin Gao, Fei Gong, Guangming Jing, Zhongshan Li, Yan Ling Shao, Lihua Zhang (2016)

Czechoslovak Mathematical Journal

A sign pattern matrix (or nonnegative sign pattern matrix) is a matrix whose entries are from the set { + , - , 0 } ( { + , 0 } , respectively). The minimum rank (or rational minimum rank) of a sign pattern matrix 𝒜 is the minimum of the ranks of the matrices (rational matrices, respectively) whose entries have signs equal to the corresponding entries of 𝒜 . Using a correspondence between sign patterns with minimum rank r ≥ 2 and point-hyperplane configurations in ℝ r - 1 and Steinitz’s theorem on the rational realizability of...

Reachability and observability of linear systems over max-plus

Michael J. Gazarik, Edward W. Kamen (1999)

Kybernetika

This paper discusses the properties of reachability and observability for linear systems over the max-plus algebra. Working in the event-domain, the concept of asticity is used to develop conditions for weak reachability and weak observability. In the reachability problem, residuation is used to determine if a state is reachable and to generate the required control sequence to reach it. In the observability problem, residuation is used to estimate the state. Finally, as in the continuous-variable...

Reachability of cone fractional continuous-time linear systems

Tadeusz Kaczorek (2009)

International Journal of Applied Mathematics and Computer Science

A new class of cone fractional continuous-time linear systems is introduced. Necessary and sufficient conditions for a fractional linear system to be a cone fractional one are established. Sufficient conditions for the reachability of cone fractional systems are given. The discussion is illustrated with an example of linear cone fractional systems.

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