Preprint series: 06-01, Reports on Analysis

MSC:

93C25 Systems in abstract spaces

34K30 Equations in abstract spaces, See also {34Gxx}

34K35 Control problems, See also {49J25, 49K25, 93C15}

47D06 One-parameter semigroups and linear evolution equations

Abstract: We show that the class of regular non-autonomous systems is invariant under perturbations by time-varying state and input delays. In particular, we give explicit formulas of the resulting input, output, and input-output maps. This result is used to solve the feedback problem for the delayed system. The relationship between the open and the closed loop system is investigated. Our results are applied to a parabolic boundary control problem with input and
state delays.

Keywords: Regular non-autonomous systems, retarded evolution equation, input delay, Lebesgue extension, feedback

Upload: 2006-01-13

Update: 2006 -01 -13