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State feedback stabilization and majorizing achievement of min-max-plus systems

The state feedback stabilization of min-max-plus systems is investigated in this note. The concepts of digraph description, (r,s)-reachability, max-plus projection direct product, etc., are introduced to deal with the stability. The sufficient condition and the necessary condition for the state feedback stabilization are presented respectively and the desired eigenvalue area is determined. Moreover, the state feedback is constructed for majorizing achievement of the stabilization and the corresponding algorithm is derived.