  In this paper, we propose a decision procedure of reachability for linear
system {\xi}' = A{\xi} + u, where the matrix A's eigenvalues can be arbitrary
algebraic numbers and the input u is a vector of trigonometric-exponential
polynomials. If the initial set contains only one point, the reachability
problem under consideration is resorted to the decidability of the sign of
trigonometric-exponential polynomial and then achieved by being reduced to
verification of a series of univariate polynomial inequalities through Taylor
expansions of the related exponential functions and trigonometric functions. If
the initial set is open semi-algebraic, we will propose a decision procedure
based on openCAD and an algorithm of real roots isolation derivated from the
sign-deciding procedure for the trigonometric-exponential polynomials. The
experimental results indicate the efficiency of our approach. Furthermore, the
above procedures are complete under the assumption of Schanuel Conjecture
