Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Singular Perturbation Methods and Time-Scale Techniques Read chapter Read first chapter

2017 | OriginalPaper | Chapter

2. Theoretical Foundation of Finite Frequency Control

Authors : Chenxiao Cai, Zidong Wang, Jing Xu, Yun Zou

Published in: Finite Frequency Analysis and Synthesis for Singularly Perturbed Systems

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Finite frequency control strategy has been proven to be an important method for modern control system. Combined with the particular frequency characteristics of the plant, many control specifications in the full frequency domain can be simplified into finite frequency ones. Commonly used tools in the frequency division are the weighting function and general Kalman-Yakubovich-Popov (GKYP) Lemma. In this chapter, some background information and useful lemmas in the field of finite frequency control have been investigated in detail.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now
previous chapter Singular Perturbation Methods and Time-Scale Techniques
next chapter Stabilization of Singularly Perturbed Systems
Literature
1.
Davidson, T., Luo, Z., Sturm, J.: Linear matrix inequality formulation of spectral mask constraints. In: Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 6, pp. 3813–3816 (2001)
2.
3.
Genin, Y., Hachez, Y., Nesterov, Y., Van Dooren, P.: Convex optimization over positive polynomials and filter design. In: Proceedings of UKACC International Conference on Control (2000)
4.
Hara, S., Iwasaki, T.: Robust PID control using generalized KYP synthesis. IEEE Control Syst. Mag. 26(1), 80–91 (2006)MathSciNetCrossRef
5.
Iwasaki, T., Hara, S., Yamauchi, H.: Dynamical system design from a control perspective: finite frequency positive realness approach. IEEE Trans. Autom. Control 48(8), 1337–1354 (2003)MathSciNetCrossRef
6.
Iwasaki, T., Hara, S., Fradkov, A.L.: Time domain interpretations of frequency domain inequalities on finite ranges. Syst. Control Lett. 54(7), 681–691 (2005)MathSciNetCrossRefMATH
7.
Iwasaki, T., Meinsma, G., Fu, M.: Generalized S-procedure and finite frequency KYP lemma. Math. Prob. Eng. 6(2–3), 305–320 (2009)MathSciNetMATH
8.
Iwasaki, T., Hara, S.: Robust control synthesis with general frequency domain specifications: static gain feedback case. Proc. Am. Control Conf. 5, 4613–4618 (2004)
9.
Iwasaki, T., Hara, S.: Generalized KYP lemma: unified frequency domain inequalities with design applications. IEEE Trans. Autom. Control 50(1), 41–59 (2005)MathSciNetCrossRef
10.
Jonsson, U.: Robustness analysis of uncertain and nonlinear systems. Ph.D. Dissertation, Department of Automatic Control, Lund Institute of Technology (1996)
11.
Luse, D.W., Ball, J.A.: Frequency-scale decoposition of \(H_\infty \) disk problems. SIAM J. Control Optimization 27, 814–835 (1989)MathSciNetCrossRefMATH
12.
13.
Megretski, A., Treil, S.: Power distribution inequalities in optimization and robustness of uncertain systems. J. Math. Syst. Estim. Control 3(3), 301–319 (1993)MathSciNetMATH
14.
Nesterov, Y.: Squared functional systems and optimization problems. In: Frenk, H., et al. (eds.) High Performance Optimization, pp. 405–440. Kluwer Academic Publishers, Dordrecht (2000)CrossRef
15.
Oloomi, H., Shafai, B.: A system theory criterion for positive real matrices. SIAM J. Control 5(171–182), 2008 (1967)MathSciNet
16.
Pipeleers, G., Vandenberghe, L.: Generalized KYP lemma with real data. IEEE Trans. Autom. Control 56(12), 2942–2946 (2011)MathSciNetCrossRef
17.
18.
19.
Willems, J.C.: Least squares stationary optimal control and the algebraic Riccati equation. IEEE Trans. Autom. Control 16(6), 621–634 (1971)MathSciNetCrossRef
20.
Yakubovich, V.A.: The S-procedure in nonlinear control theory. Vestn. Leningrad Univ. 1, 62–77 (1971)MathSciNetMATH
21.
Yakubovich, V.A.: Nonconvex optimization problem: the infinite-horizon linear-quadratic control problem with quadratic constraints. Syst. Control Lett. 19(1), 13–22 (1992). (2010)MathSciNetCrossRefMATH
Metadata
Title
Theoretical Foundation of Finite Frequency Control
Authors
Chenxiao Cai
Zidong Wang
Jing Xu
Yun Zou
Copyright Year
2017
Book
Finite Frequency Analysis and Synthesis for Singularly Perturbed Systems

Print ISBN: 978-3-319-45404-7

Electronic ISBN: 978-3-319-45405-4

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-45405-4_2