A Characterization of the Eigenvalue of a General (Min,Max, +)-System
Discrete Event Dynamic Systems
A Cycle Time Computing Algorithm and its Application in the Structural Analysis of Min-max Systems
Discrete Event Dynamic Systems
Globally optimal solutions of max---min systems
Journal of Global Optimization
Time separations of cyclic event rule systems with min-max timing constraints
Theoretical Computer Science
Independent cycle time assignment for min-max systems
International Journal of Automation and Computing
A survey of the theory of min-max systems
ICIC'05 Proceedings of the 2005 international conference on Advances in Intelligent Computing - Volume Part II
| Hi-index | 5.23 |
In this paper we consider bipartite (min, max, +)-systems. We present conditions for the structural existence of an eigenvalue and corresponding eigenvector for such systems, where both the eigenvalue and eigenvector are supposed to be finite. The conditions are stated in terms of the system matrices that describe a bipartite (min, max, +)-system. Structural in the previous means that not so much the numerical values of the finite entries in the system matrices are important, rather than their locations within these matrices. The conditions presented in this paper can be seen as an extension towards bipartite (min, max, +)-systems of known conditions for the structural existence of an eigenvalue of a (max, +)-system involving the (ir)reducibility of the associated system matrix. Although developed for bipartite (min, max, +)-systems, the conditions for the structural existence of an eigenvalue also can directly be applied to general (min, max, +)-systems when given in the so-called conjunctive or disjunctive normal form.