Controlled Invariance and Dynamic Feedback for Systems over Semirings

The concept of (A, B)-invariant subspace is the fundamental concept of the geometric approach of control design. It has been extended by many authors to that of (A, B)-invariant module or semimodule, for the sake of extending the solution of various control problems to the case of systems over rings or semi rings. In this paper is discussed the use of dynamic feedback control laws for systems over semirings, and it is shown that an (A, B)-invariant semimodule over a commutative semiring can be made invariant for the closed-loop system by dynamic feedback.