Some results on the feedback control of max-plus linear systems under state constrains

The aim of this paper is to study a control problem for a class of restriction, which appears in design of feedback controllers for timed discrete event systems, taking performance (eigenvalue of the closed loop matrix) and realization issues into account. The obtained results are based on properties of the system and the restriction matrices. For a given class of theses matrices, it is shown that a causal feedback can be computed by solving linear equations. In order to illustrate the applicability of the results, we solve a small traffic light problem.