A note on invariant time linear system over semiring

A linear time-invariant system is a system that satisfies the property that the input-output characteristics do not change with time. A semiring is an algebraic structure defined as a non-empty set with two binary operations (addition and multiplication). In addition, a semiring is a commutative monoid, and it is a semigroup for multiplication. The specific purpose of this research proposal is to determine the necessary or sufficient conditions for the completion of a linear time-invariant system on a semiring. The problem of linear time-invariant system is limited to state u = 1, so we get Ax = c. The linear system has a solution if the matrix A has an inverse. A semiring is an associative structure, so the inverse of the matrix over the semiring is viewed from the matrix partition.