NUMERICAL APPROXIMATIONS FOR HEREDITARY-SYSTEMS WITH INPUT AND OUTPUTDELAYS - CONVERGENCE RESULTS AND CONVERGENCE-RATES

In this paper, the averaging approximation scheme for linear retarded functional differential equations with delays in control and observati on 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 e stimate of convergence rate of the approximating semigroups are establ ished. These extend results due to Banks and Burns [SIAM J. Control Op tim., 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 ar e excluded is that unbounded input and output operators must be dealt with in the abstract formulation. Moreover, in the presence of the unb oundedness of the input and output operators, new convergence results of the state solutions and the output are also obtained.