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IMA Journal of Mathematical Control and Information 1984 1(3):283-306; doi:10.1093/imamci/1.3.283
© 1984 by Institute of Mathematics and its Applications
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On the Evaluation of Cost Functionals, with Particular Emphasis on Time-delay Systems

K. WALTON1 and H. GORECKI2

1School of Mathematics, University of Bath Bath, BA2 7AY England
2Academy of Mining and Metallurgy, Institute for Automatic Systems, Engineering and Telecommunications, al. Mickiewicza 30, 30-059 Krakow, Poland

It is useful to have closed-form expressions for the cost functional where e(t) is a function representing error in a control system. The paper shows how the well-known results for delay-free systems may be extended to the time-delay case and a survey of various methods is given. Finally, an alternative derivation of the Routh—Hurwitz stability criteria for the delay-free case is given. This makes use of the close relationship between the above integrals and stability theory.


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