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Note on the persistent property of a feedback control system with delays. (English) Zbl 1187.34106

Summary: By developing some new analysis techniques, we show that the following feedback control system of differential equations with delays is permanent.

dN(t) dt=r(t)N(t)1-N 2 (t-τ 1 (t)) k 2 (t)-c(t)u(t-τ 2 (t)),du(t) dt=-a(t)u(t)+b(t)N(t-τ 1 (t)),

where τ 1 ,τ 2 ,a,b,c,r,kC(,(0,+)) are ω-periodic functions, which means that feedback control variable has no influence on the persistent property of the above system.

MSC:
34K25Asymptotic theory of functional-differential equations
93B52Feedback control
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