On the Completely Controllability of One Stage by Stage Changing Linear Stationary System Using a Dynamic Controller

The problem of completely controllability of stage by stage changing linear stationary dynamic systems using a dynamic controller is considered. A definition of the completely controllability of stage by stage changing linear systems using a dynamic controller is given. A specific stage by stage changing completely controllable system is considered, which is formed at certain intervals of time by not completely controllable systems. The criterion of completely controllability of stage-by-stage linear stationary systems using a dynamic controller, which is expressed directly through the parameters of the original systems, is used. Based on this criterion, for arbitrarily given initial and final states of a stage by stage changing system, the existence of a dynamic controller is shown. An explicit analytical expression is constructed for the dynamic controller, which generates the movement of the system that satisfies the conditions of the problem. As an illustration, a numerical experiment was performed with the construction of corresponding graphs.