The Perturbed Adjoint Operator for Linear Hereditary Differential Systems with Perturbed Delay in Control
In the paper we present the new perturbation results for the adjoint operator of the infinitesimal generator of a strongly continuous semigroup of linear operators for linear differential-delay equations (DDE) with delay in the state of the system and in the control. The achieved perturbation results are particularly important because the considered perturbations of the delay in the control can be also of finite magnitude, which is the case frequently encountered in the real-world problems. Our results enable in an easy way to achieve the sensitivity results for the dual problem of linear-quadratic optimal control problem: the so called filtering with delay in observation (see ).
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