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Harmonic forcing for linear distributed parameter systems. (English) Zbl 0906.93028

The authors consider a linear input-output control system of the form \(\dot z = Az+bu\), \(z(0) = z_0\), \(y=cz\) where \(A\) is the infinitesimal generator of a \(C_0\) semigroup in a Hilbert space \(Z\) and \(b\:{\mathbb R}\to Z\), \(c\:Z\to {\mathbb R}\) are bounded operators. Sufficient conditions are given under which a harmonic input \(u\) produces a nontrivial periodic output \(y\) with the same period.

MSC:

93C25 Control/observation systems in abstract spaces
35B10 Periodic solutions to PDEs
93A99 General systems theory
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