Performance analysis of linear systems over semiring with additive inputs

This paper deals with the computation of a maximal flow in single input single output (max, +) linear systems. Assuming known a system composed of some subsystems - each one being described by a transfer function and some secondary inputs interfering with the principal flow on consecutive sub-systems, the computation of a maximal principal output is addressed. Transfer functions, inputs and outputs are represented by periodical series in a semiring of formal series, namely Nopfmindelta. Previously, it is shown that the Hadamard product of such series allows to compute the addition of inputs, and that this product is both residuated and dually residuated. These properties are used to compute the maximal principal output. An example concludes the paper and allows to illustrate the efficiency of the proposed approach.