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The Perturbed Adjoint Operator for Linear Hereditary Differential Systems with Perturbed Delay in Control

  • Ludvik Bogataj
Conference paper

Abstract

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 [4]).

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References

  1. [1]
    L. Bogataj, The adjoint operator of the infinitesimal generator for the linear differential-difference equation with delays in the state and in the control. Glasnik Matematicki, 24 (1989), pp.349–354.Google Scholar
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    L. Bogataj, Sensitivity of linear-quadratic systems with delay in the state and in the control for perturbation of the system matrices, Glasnik Matematicki, 24 (1989), pp.355–360.Google Scholar
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    L. Bogataj, The estimation of the influence of uncertain delay in the control on the objective function, Matematicki Glasnik, 25 (1990), pp.721–730.Google Scholar
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    A. Ichikawa, Quadratic control of evolution equations with delays in control, SIAM J. Control and Optimization, 20 (1982).pp. 645–668.CrossRefGoogle Scholar
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    R. Vinter, On the evolution of the state of linear differential delay equations in M2; Properties of generator, J.lnst.Math.Appl. 21 (1978), pp. 13–23.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Ludvik Bogataj
    • 1
  1. 1.Faculty of EconomicsUniversity of LjubljanaLjubljanaSlovenia

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