On control of degenerate distributed systems
Марина Васильевна Плеханова, Vladimir Evgen'evich Fedorov · Ufimskii Matematicheskii Zhurnal · 2014
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 -controllability in time and of -controllability in a free time in terms of the operators involved in the equation.General results are used for studying of -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.