A two-step procedure for stable time-suboptimal control is proposed. The procedure involves the use of two feedback gain matrices. The first matrix is determined to transfer the system from a given state to the vicinity of the desired state in minimum time. Then a switch is made to a second feedback gain matrix obtained from shifting of eigenvalues For maximum stability. The viability of the proposed procedure is demonstrated with a linear six-p!ate gas absorber and a non-linear two-stage CSTR system.