AbstractThis paper treats systems in state variable formulation with non‐constant, parameter controlled system matrices. The synthesis of a system with controlled eigenvalues (ECS) is given. The synthesized system is a commutative bilinear system. Its solution has a closed form and is based on the solution of just one time invariant system although as many arbitrary time functions are involved as the system has independent states. The ECS is homologous to any system with a system matrix being an arbitrary, possibly time‐dependent function of a single constant system matrix.All results are deduced for multiple eigenvalues of the system matrix including single eigenvalues as a special case. They are fully analogous to the solution of time invariant systems by means of the Laplace transformat