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Balachandran, K.; Marshal Anthoni, S.

Controllability of second-order semilinear neutral functional differential systems in Banach spaces. (English) Zbl 0990.93007

Comput. Math. Appl. 41, No. 10-11, 1223-1235 (2001).
Semilinear second-order neutral functional dynamical systems defined in infinite-dimensional Banach spaces are considered. It is generally assumed that the state equation contains both a linear part without delays and a nonlinear part containing delays. First of all the definition of exact relative controllability in a given finite-time interval is presented. Next, using Leray-Schauder’s fixed-point theorem, sufficient conditions for controllability are formulated and proved. In the proofs of the main results, the semigroup theory of linear operators in Banach spaces is used. Moreover, several remarks and comments concerning controllability problems for infinite-dimensional control systems with delays are presented. The relationship to results existing in the literature are also given. Finally, it should be pointed out that similar controllability problems have been recently considered in the papers [the authors and J. Y. Park, Bull. Korean Math. Soc. 35, No. 1, 1-13 (1999; Zbl 0935.93013)] and [J. Y. Park and H. K. Han, ibid. 34, 411-419 (1997; Zbl 0889.93008)].
Reviewer: J.Klamka (Katowice)

Cited in 21 Documents

MSC:

93B05 Controllability
93C23 Control/observation systems governed by functional-differential equations
34K30 Functional-differential equations in abstract spaces
34K35 Control problems for functional-differential equations
34K40 Neutral functional-differential equations

Keywords:

semilinear control systems; second-order neutral functional dynamical systems; delays; exact relative controllability; Leray-Schauder fixed-point theorem; semigroup theory of linear operators in Banach spaces

Citations:

Zbl 0935.93013; Zbl 0889.93008
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\textit{K. Balachandran} and \textit{S. Marshal Anthoni}, Comput. Math. Appl. 41, No. 10--11, 1223--1235 (2001; Zbl 0990.93007)
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References:

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