A Remark on Inseparability of Min–Max Systems

Q. Zhao
2004 IEEE Transactions on Automatic Control  
Min-max systems, or min-max-plus systems are algebraic models of Discrete Event Dynamic Systems. They are non-linear extensions of the well known linear max-plus system models. The structural property 'inseparability' of min-max systems was proposed by us in a recent paper. It turns out that inseparability is equivalent to the property of 'irreducibility' proposed recently by van der Woude and Subiono, although the two properties appear in very different forms. We will prove this fact here.
more » ... x Terms Min-max systems, inseparability, irreducibility, structural property. I. INTRODUCTION Discrete event systems in which the operations min, max and plus appear simultaneously are known as min-max systems or min-max-plus systems. A variety of problems arising in digital circuits, computer networks and automated manufacturing plants can be described using these models (see [1] , [2], [3] and references therein for more detailed discussions on the applications of min-max systems). Theoretically, they are non-linear extensions of the well known linear max-plus system models [4] .
doi:10.1109/tac.2004.829611 fatcat:k3o63u4xtjebjc2pkdfgyzxn7y