Systems with Distributed Delay

  • Vladimir L. Kharitonov
Part of the Control Engineering book series (CONTRENGIN)


The last chapter of the first part of the book is dedicated to the retarded type linear time-delay systems with distributed delay. First, quadratic functionals with a prescribed time derivative along the solutions of such a system are introduced and Lyapunov matrices that define the functional are derived. Then, such issues as the existence and uniqueness of Lyapunov matrices are studied. A numerical procedure for the computation of Lyapunov matrices is proposed. It is shown that in some cases the computation of the matrices is reduced to the solution of a boundary value problem for an auxiliary system of linear matrix ordinary differential equations. Complete type quadratic functionals are defined, and various application of the functionals are discussed.


Lyapunov Matrices Linear Matrix Ordinary Differential Equations Quadratic Functionals Complete Type Boundary Value Conditions 
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© Springer Science+Business Media, LLC 2013

Authors and Affiliations

  • Vladimir L. Kharitonov
    • 1
  1. 1.Faculty of Applied Mathematics and Processes of ControlSaint Petersburg State UniversitySaint PetersburgRussia

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