Abstract
Stationary and nonstationary control hereditary systems are investigated in the paper. The problem of relative controllability for nonstationary control hereditary systems is studied, the problem of minimum number of inputs tor relatively controllable hereditary system, the problem of controllability with respect to the initial function, the problem ot control by Lyapunov's index of linear nonstationary system are investigated. The problem of the complete controllability for hereditary systems and the adjacent controllability problems are considered. The results are illustrated with the examples.
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