Abstract
Consideration was given to the controllable system of ordinary linear differential equations with the matrix at the derivative of the desired vector function that is identically degenerate in the domain of definition. For the one-input systems, the questions of stabilizability and solvability of the control problem by the Lyapunov indices were studied for the stationary and nonstationary cases. Analysis was based on the assumptions providing existence of the so-called "equivalent form" where the "algebraic" and "differential" parts are separated. An arbitrarily high index of insolvability and variable rank of the matrix at the derivative were admitted.
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