On Controllability of Degenerate Distributed Systems

We study the controllability of linear distributed control systems described by differential equations in Banach spaces with a degenerate operator at the derivative. A homogeneous part of equations has a degenerate strongly continuous resolving semigroup. For such system with, generally speaking, a time-dependent bounded operator at the control function we find the criteria of ε-controllability in time T and of ε-controllability in a free time in terms of the operators involved in the equation. General results are used for studying of ε-controllability of the considered systems with a finite-dimensional input. The obtained conditions are demonstrated by examples of control systems described by partial differential equations and systems of equations unsolved with respect to the time derivative.