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Meccanica

, Volume 3, Issue 1, pp 3–6 | Cite as

A differential equation for the minors of the state-transition matrix of linear systems

  • Giuseppe Basile
  • Giovanni Marro
Article
  • 46 Downloads

Summary

A differential equation for the minors of the state transition matrix of linear time-invariant systems is established.

An example is then presented, where the differential equation is employed in order to check the existence of the extremal control of a linear system with a performance index given by the integral of a quadratic form.

Keywords

Differential Equation Mechanical Engineer State Transition Linear System Civil Engineer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Sommario

Si stabilisce un'equazione differenziale per i minori della matrice di transizione dei sistemi lineari stazionari.

Si illustra quindi un esempio, in cui tale equazione differenziale viene impiegata per verificare l'esistenza del controllo estremale di un sistema lineare con indice di comportamento dato dall'integrale di una forma quadratica.

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References

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    F. R. Gantmacher,Matrix Theory, Chelsea, New York, 1959.Google Scholar
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    S. Cherubino,Calcolo delle matrici, Ediz. Cremonese, Roma, 1957.Google Scholar
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    C. Lanczos,Linear differential operators, Van Nostrand, London, 1961.Google Scholar
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    W. Kipiniak,Dynamic optimization and control, J. Wiley & Sons, New York, 1961.Google Scholar
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    M. Athans andP. Falb,Optimal Control, Mc Graw-Hill, New York, 1966.Google Scholar
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    A. M. Letov,Analytic controller design, I, II, III;Automation and Remote Control, english transl. of Automatika i Telemekhanika, Vol. 21, no. 4, pp. 436–441; no. 5, pp. 561–568; no. 6, pp. 661–665, 1960.Google Scholar

Copyright information

© Tamburini Editore s.p.a 1966

Authors and Affiliations

  • Giuseppe Basile
    • 1
  • Giovanni Marro
    • 2
  1. 1.Istituto di ElettrotecnicaUniversità di GenovaItaly
  2. 2.Centro Calcoli e ServomeccanismiUniversità di BolognaItaly

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