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Controllability of abstract neutral functional differential systems with infinite delay. (English) Zbl 1001.93005

The authors study the controllability of neutral functional differential systems with infinite delay of the form \[ {d\over dt}\{x(t)-g(t,x_t)\}=Ax(t)+Bu(t)+f(t,x_t), t\in [0,b], x_0=\phi, \] where \(f,g: [0,b]\times {\mathcal B}\to X\) are continuous functions, \({\mathcal B}\) is an abstract phase space introduced in [J. K. Hale and J. Kato, Funkc. Ekvacioj, Ser. Int. 21, 11-41 (1978; Zbl 0383.34055)], \(A\) is the infinitesimal generator of a \(C_0\) semigroup of bounded linear operators on a Banach space \(X,\) the control function \(u(\cdot)\) is given in \(L^2([0,b],U),\) which is a Banach space of admissible control functions, with \(U\) as a Banach space. Finally, \(B\) is a bounded linear operator from \(U\) into \(X.\) An example which illustrates the theoretical result is also presented.

MSC:

93B05 Controllability
93C25 Control/observation systems in abstract spaces
34K30 Functional-differential equations in abstract spaces
34K40 Neutral functional-differential equations

Citations:

Zbl 0383.34055
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