THEORY AND ALGORITHMS ON PERIOD ASSIGNMENT OF DISCRETE-EVENT DYNAMIC-SYSTEMS

For a discrete-event dynamic system described by max algebra as X(k) = X(k - 1)A + U(k)B, all the eigenvalues lambda(i), 1 less-than-or-equal-to i less-than-or-equal-to omega, in the right upper triangular standard form of A are called periods. It is proved in this paper that the periods can be assigned arbitrarily in [lambda(i), + infinity) by state feedback U(k) = X(k)K if and only if A and B have matching standard forms. Algorithms on period assignment are also given.