Math. Model. Nat. Phenom.
Volume 12, Number 6, 2017Special Issue - Nonlocal and delay equations
|Page(s)||91 - 105|
|Published online||30 December 2017|
Stabilization by delay distributed feedback control
Department of Mathematics, Ariel University,
Accepted: 2 October 2017
is proposed. Under corresponding conditions on the coefficients α1, α2, β1 and β2 the first equation is exponentially stable if the delays τ1 (t) and τ2 (t) are large enough and the second equation is exponentially stable if these delays are small enough. On the basis of these results, assertions on stabilization by distributed input control are proven. It should be stressed that stabilization of this sort, according to common belief, requires a damping term in the second order differential equation. Results obtained in this paper demonstrate that this is not the case.
Mathematics Subject Classification: 34K20
Key words: Exponential stability / stabilization / integro-differential equations / distributed delays / distributed inputs
© EDP Sciences, 2017
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