In the class of linear algorithms of linear stationary multi-connected plants control the subclass is distinguished of quasi-terminal algorithms with implicit aiming at the boundary conditions moving along the program of the required change of the state vector coordinates and being at a xed interval from the current time. Aiming is realized by calculating the programs of changing the future control vector components in the form of power series segments that depend on the future time and provide a solution of the two-point boundary value problem. In idealized model conditions of the complete controllability and the availability of an accurate information about the control plant state and equations, as well as of the instantaneous and accurate implementation of the calculated commands, the quasi-terminal algorithm provides the asymptotic stability of a closed multi-connected system and as high pre-set rate of transients convergence as needed, regardless of whether the control plant model is stable. The relatively simple and easy to implement in MATLAB non-optimization method of algorithm synthesis is suggested based on the use of the matrix representation of the control plant model in the state space and of the apparatus of exponential functions of matrices. Quasi-terminal algorithms can be used in multiconnected stabilization systems and, in particular, in stabilization systems of mobile terminal plants with respect to trajectories calculated by the terminal control system.