Abstract
ABSTRACTRobustness analysis is a fundamental problem in the area of formal method, systems theory and performance evaluation. This paper investigates the global robustness of max-plus linear systems, which requires all state variables are entirely unaffected by the bounded parameter perturbations. The variable element is introduced to describe the global robustness. The relationship between solvable entries and solutions of systems of max-plus linear equations is further studied to find the variable elements of max-plus linear systems. It is pointed out that any non-solvable entry is a variable element. At the same time, the global robustness is used to analyse the stability of gene regulatory networks in biology systems and the time invariance of production processes in flexible manufacturing systems. Some numerical examples are given to illustrate the results.
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