Abstract
In this paper, the averaging approximation scheme for linear retarded functional differential equations with delays in control and observation is considered in the context of the state space theory developed by Pritchard and Salamon [SIAM J. Control Optim., 25 (1987), pp. 121–144]. Using known results from linear semigroup theory, convergence and estimate of convergence rate of the approximating semigroups are established. These extend results due to Banks and Burns [SIAM J. Control Optim., 16 (1978), pp. 169–208] and Lasiecka and Manitius [SIAM J. Numer. Anal., 25 (1988), pp. 883–907] on hereditary systems with delays in state, to the case when delays in control and observation are included. The main difference from the case when delays in input and output are excluded is that unbounded input and output operators must be dealt with in the abstract formulation. Moreover, in the presence of the unboundedness of the input and output operators, new convergence results of the state solutions and the output are also obtained.
Published Version
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