ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

On H2 Norm of the Transfer Matrix of Neutral Type Time-delay System


Victoria Sumacheva

St. Petersburg State University,
faculty of Applied Mathematics and Control Processes
postgraduate student

Vladimir Kharitonov

St. Petersburg State University,
faculty of Applied Mathematics and Control Processes
D.Sc., Professor of Department of Control Theory


The problem of computing H2 norm of the transfer matriх of neutral type time-delay systems is considered. It is known that the Lyapunov matrices can be used to compute H2 norm of delay free linear time invariant systems. In this work we showed that H2 norm of the transfer matrix of neutral type time-delay system may be expressed in the terms of the Lyapunov matrices for time-delay systems and obtained the explicit expression for it.


  1. Bellman R., Cooke K. Differential-Difference Equations. New York/London: Academic Press, 1963. 462 p
  2. Jarlebring E., Vanbierviet J., Michiels W. [Explicit expression for the H2 norm of time-delay system based on the delay Lyapunov equation]. Proceedings of the 49th IEEE Conference on Decision and Control, Atlanta, USA, 2010, pp. 164-169
  3. Kharitonov V. L. Time-Delay Systems: Lyapunov Functional and Matrices. Boston: Birkhauser, 2013. 327 p
  4. Lancaster P. Theory of Matrices. New York/London: Academic Press, 1969. 326 p
  5. Zhou K., Doyle J. C., Glover K. Robust and Optimal Control. New York, Engelwood Cliffs: Prentice Hall, 1996. 586 p
  6. Lavrentev M. A., Shabat B. V. Metody teorii funktsiy kompleksnogo peremennogo [Methods of the theory of functions of a complex variable]. Moscow, Nauka Publ., 1973. 749 p
  7. Elsgolts L. E., Norkin S. B. Vvedenie v teoriu differentsialnih uravneniy s otklonyaushimsya argumentom [Introduction to the theory of differential equations with deviating argument]. Moscow, Nauka Publ., 1971. 296 p

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