Geodesic
On control of degenerate distributed systems
Ufa mathematical journal, Tome 6 (2014) no. 2, pp. 77-96

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We study the control 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 time-dependent bounded operator at the control function we find the criteria of the $\varepsilon$-control for time $T$ and of the $\varepsilon$-control in for a free time in terms of the operators involved in the equation. General results are used for studying of the $\varepsilon$-control 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.
Keywords: control system, degenerate evolution equation, control.
Mots-clés : Sobolev type equation 
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     author = {M. V. Plekhanova and V. E. Fedorov},
     title = {On control  of degenerate distributed systems},
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M. V. Plekhanova; V. E. Fedorov. On control  of degenerate distributed systems. Ufa mathematical journal, Tome 6 (2014) no. 2, pp. 77-96. http://geodesic.mathdoc.fr/item/UFA_2014_6_2_a5/