Conditions for the structural existence of an eigenvalue of a bipartite (min,max,+)-system

Woude, Jacob van der; Subiono,

doi:10.1016/s0304-3975(02)00229-3

Cited by 20 publications

(12 citation statements)

References 12 publications

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“…The new circuit is denoted by t(i)u j(i) xj · · · xi. If the new circuit passes a point xj in some Xj , by (10), then there are the white color (containing the r * (j)-th color) path from t(i) to xj, passing u j(i) , and the r * (i)-th color path from xj to t(i). Similar to (18) and (19), we have…”

Section: Independent Assignmentmentioning

confidence: 99%

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Independent cycle time assignment for min-max systems

Chen

Tao

2010

Int. J. Autom. Comput.

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A variety of problems in digital circuits, computer networks, automated manufacturing plants, etc., can be modeled as min-max systems. The cycle time is an important performance metric of such systems. In this paper, we focus on the cycle time assignment of min-max systems which corresponds to the pole assignment problem in traditional linear control systems. For the minmax system with max-plus inputs and outputs, we show that the cycle time can be assigned disjointedly by a state feedback, if and only if the system is reachable. Furthermore, a necessary and sufficient condition for the cycle time to be assigned independently by a state feedback is given. The methods are constructive, and some numerical examples are given to illustrate how the methods work in practice.

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Section: Independent Assignmentmentioning

confidence: 99%

“…Cochet-Terransson et al [9] obtained a constructive eigenvector theorem for general min-max systems. van der Woude and Subiono [10] presented a necessary and sufficient condition of the structural existence of an eigenvalue and a corresponding eigenvector for bipartite min-max systems.…”

Section: Introductionmentioning

confidence: 99%

Independent cycle time assignment for min-max systems

Chen

Tao

2010

Int. J. Autom. Comput.

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“…If one imposes a limitation on the above structure by stipulating that any parameter a can only appear in a term like x i + a (this limitation does not result in any loss of expressive power in that all min-max functions can still be formed by using this structure), then the SEE property becomes the inseparability introduced by Zhao in [17]. For bipartite min-max functions [1], the SEE property was studied by Olsder in [18] and later van der Woude and Subiono gave in [19] a sufficient and necessary condition called irreducibility in the language of max-plus algebra and min-plus algebra.…”

Section: Structural Propertiesmentioning

confidence: 99%

A Survey of the Theory of Min-Max Systems

Cheng

2005

Lecture Notes in Computer Science

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Abstract. Min-max systems are discrete event systems whose timing involves the maximum, minimum, and addition operations. In recent years, progresses have been made in such topics as cycle time computation, ultimate periodicity of trajectories, structural properties, cycle time assignment, etc. They are surveyed in this paper. Furthermore, as an attempt to open new directions for further research we propose two new models referred to as and-or net and and-or event graph. It is found that timed and-or event graphs can be algebraically described by minmax systems. We hope that these new models would accommodate more new results.

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“…Gaubert and Gunawardena [18,19] proved the Duality Theorem which plays an important part in the proof of the existence of a fixed point of min-max-plus systems. van der Woude and Subiono [20] investigated the conditions for structural existence of an eigenvalue of min-max-pus systems.…”

Section: Introductionmentioning

confidence: 99%