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:
On the Codimension of the Singularity at the Origin for Networked Delay Systems Read chapter Read first chapter

2016 | OriginalPaper | Chapter

5. Analysis of Bilinear Systems with Sampled-Data State Feedback

Authors : Hassan Omran, Laurentiu Hetel, Jean-Pierre Richard, Françoise Lamnabhi-Lagarrigue

Published in: Delays and Networked Control Systems

Publisher: Springer International Publishing

Log in

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

search-config
loading …

Abstract

In this chapter we consider the stability analysis of bilinear systems controlled via a sampled-data state feedback controller. Sampling periods may be time-varying and subject to uncertainties. The goal of this study is to find a constructive manner to estimate the maximum allowable sampling period (MASP) that guarantees the local stability of the system. Stability criteria are proposed in terms of linear matrix inequalities (LMI).

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

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter General Formula for Event-Based Stabilization of Nonlinear Systems with Delays in the State
next chapter On the Stability Analysis of Sampled-Data Systems with Delays
Footnotes
2
The equivalence between the representations in (5.5) and (5.6) is given in [10] (Theorem 1.29).
 
Literature
1.
F. Amato, C. Cosentino, A. Fiorillo, A. Merola, Stabilization of bilinear systems via linear state-feedback control. IEEE Trans. Circuits Syst. II: Express Briefs 56(1), 76–80 (2009)CrossRef
2.
F. Amato, C. Cosentino, A. Merola, Stabilization of bilinear systems via linear state feedback control, in 15th Mediterranean Conference on Control Automation, MED ’07 (2007)
3.
V. Andrieu, S. Tarbouriech, Global asymptotic stabilization for a class of bilinear systems by hybrid output feedback. IEEE Trans. Autom. Control 58(6), 1602–1608 (2013)MathSciNetCrossRef
4.
N. Athanasopoulos, G. Bitsoris, Unconstrained and constrained stabilisation of bilinear discrete-time systems using polyhedral Lyapunov functions. Int. J. Control 83(12), 2483–2493 (2010)MathSciNetCrossRefMATH
5.
C. Bruni, G.D. Pillo, G. Koch, Bilinear systems: An appealing class of "nearly linear" systems in theory and applications. IEEE Trans. Autom. Control 19(4), 334–348 (1974)MathSciNetCrossRefMATH
6.
D. Carnevale, A. Teel, D. Nešić, Further results on stability of networked control systems: a Lyapunov approach, in American Control Conference (2007)
7.
D. Carnevale, A. Teel, D. Nešić, A Lyapunov proof of an improved maximum allowable transfer interval for networked control systems. IEEE Trans. Autom. Control 52(5), 892–897 (2007)MathSciNetCrossRef
8.
M.-S. Chen, Y.-Z. Chen, Normalised quadratic controls for a class of bilinear systems. IEE Proc. Control Theory Appl. 149(6), 520–524 (2002)CrossRef
9.
M.-S. Chen, Y.-R. Hwang, Y.-J. Kuo, Exponentially stabilizing division controllers for dyadic bilinear systems. IEEE Trans. Autom. Control 48(4), 106–110 (2003)MathSciNetCrossRef
10.
F. Christophersen, Optimal Control of Constrained Piecewise Affine Systems (Springer, Lecture Notes in Control and Information Sciences, 2007)
11.
D. Elliott, Bilinear Control Systems Matrices in Action, vol.169 of Applied Mathematical Sciences (Springer, 2009)
12.
M. Espana, I. Landau, Reduced order bilinear models for distillation columns. Automatica 14(4), 345–355 (1978)CrossRef
13.
C. Fiter, L. Hetel, W. Perruquetti, J.-P. Richard, A state dependent sampling for linear state feedback. Automatica 48(8), 1860–1867 (2012)MathSciNetCrossRefMATH
14.
F. Forni, S. Galeani, D. Nešić, L. Zaccarian, Event-triggered transmission for linear control over communication channels. Automatica 50(2), 490–498 (2013)MathSciNetCrossRef
15.
16.
E. Fridman, A. Seuret, J.-P. Richard, Robust sampled-data stabilization of linear systems: an input delay approach. Automatica 40(8), 1441–1446 (2004)MathSciNetCrossRefMATH
17.
18.
19.
R. Goebel, R. Sanfelice, A. Teel, Hybrid Dynamical Systems: Modeling, Stability, and Robustness (Princeton University Press, 2012)
20.
L. Gruyitch, J.-P. Richard, P. Borne, J.-C. Gentina, Stability domains (Chapman&Hall\(\backslash \)CRC, 2004)
21.
L. Guo, H. Schwarz, A control scheme for bilinear systems and application to a secondary controlled hydraulic rotary drive, in IEEE Conference on Decision and Control (CDC) (1989)
22.
23.
L. Hetel, A. Kruszewski, W. Perruquetti, J.P. Richard, Discrete and intersample analysis of systems with aperiodic sampling. IEEE Trans. Autom. Control 56(7), 696–1701 (2011)MathSciNetCrossRef
24.
T. Hu, A nonlinear-system approach to analysis and design of power-electronic converters with saturation and bilinear terms. IEEE Trans. Power Electron. 26(2), 399–410 (2011)CrossRef
25.
26.
D. Kang, S. Won, Y.J. Jang, Guaranteed cost control for bilinear systems by static output feedback. Appl. Math. Comput. 219(14), 7398–7405 (2013)MathSciNetMATH
27.
I. Karafyllis, C. Kravaris, Global stability results for systems under sampled-data control. Int. J. Robust Nonlinear Control 19(10), 1105–1128 (2008)MathSciNetCrossRefMATH
28.
M. Khlebnikov, Quadratic stabilization of bilinear control systems, in European Control Conference (ECC) (2015)
29.
30.
31.
F. Mazenc, M. Malisoff, T.N. Dinh, Robustness of nonlinear systems with respect to delay and sampling of the controls. Automatica 49(6), 1925–1931 (2013)MathSciNetCrossRef
32.
R. Mohler, Natural bilinear control processes. IEEE Trans. Syst. Sci. Cybern. 6(3), 192–197 (1970)CrossRefMATH
33.
R. Mohler, Bilinear Control Processes: With Applications to Engineering, Ecology, and Medicine (Academic Press, Mathematics in Science and Engineering, 1974)
34.
R. Mohler, Nonlinear Systems, vol. 2: Applications to Bilinear Control (Prentice Hall, 1991)
35.
R. Mohler, A. Khapalov, Bilinear control and application to flexible a.c. transmission systems. J. Optim. Theory Appl. 105(3), 621–637 (2000)MathSciNetCrossRefMATH
36.
R. Mohler, W. Kolodziej, An overview of bilinear system theory and applications. IEEE Trans. Syst. Man Cybern. 10(10), 683–688 (1980)MathSciNetCrossRefMATH
37.
P. Naghshtabrizi, J.P. Hespanha, A.R. Teel, Exponential stability of impulsive systems with application to uncertain sampled-data systems. Syst. Control Lett. 57(5), 378–385 (2008)MathSciNetCrossRefMATH
38.
D. Nešić, A. Teel, Input-output stability properties of networked control systems. IEEE Trans. Autom. Control 49(10), 1650–1667 (2004)MathSciNetCrossRefMATH
39.
D. Nešić, A. Teel, D. Carnevale, Explicit computation of the sampling period in emulation of controllers for nonlinear sampled-data systems. IEEE Trans. Autom. Control 54(3), 619–624 (2009)MathSciNetCrossRef
40.
C. Olalla, I. Queinnec, R. Leyva, A. El Aroudi, Optimal state-feedback control of bilinear dc-dc converters with guaranteed regions of stability. IEEE Trans. Ind. Electron. 59(10), 3868–3880 (2012)CrossRef
41.
H. Omran, L. Hetel, J.-P. Richard, F. Lamnabhi-Lagarrigue, Stability of bilinear sampled-data systems with an emulation of static state feedback, in IEEE Conference on Decision and Control (CDC) (2012)
42.
H. Omran, L. Hetel, J.-P. Richard, F. Lamnabhi-Lagarrigue, Stability analysis of bilinear systems under aperiodic sampled-data control. Automatica 50(4), 1288–1295 (2014)MathSciNetCrossRefMATH
43.
P. Pardalos, V. Yatsenko, Optimization and Control of Bilinear Systems, vol.11 of Springer Optimization and Its Applications (Springer, 2008)
44.
E. Ryan, N. Buckingham, On asymptotically stabilizing feedback control of bilinear systems. IEEE Trans. Autom. Control 28(8), 863–864 (1983)CrossRefMATH
45.
46.
H. Sira-Ramírez, R. Silva-Ortigoza, Control Design Techniques in Power Electronics Devices (Springer, 2006)
47.
C.W. Tao, W.-Y. Wang, M. Chan, Design of sliding mode controllers for bilinear systems with time varying uncertainties. IEEE Trans. Syst. Man Cybern.-Part B: Cybern. 34(1), 639–645 (2004)CrossRef
48.
S. Tarbouriech, I. Queinnec, T. Calliero, P.L.D. Peres. Control design for bilinear systems with a guaranteed region of stability: an LMI-based approach, in 17th Mediterranean Conference on Control and Automation, MED ’09 (2009)
49.
W. Zhang, Stability analysis of networked control systems. PhD thesis. Departement of Electrical Engineering and Computer Science, Case Western Reserve University (2001)
Metadata
Title
Analysis of Bilinear Systems with Sampled-Data State Feedback
Authors
Hassan Omran
Laurentiu Hetel
Jean-Pierre Richard
Françoise Lamnabhi-Lagarrigue
Copyright Year
2016
Book
Delays and Networked Control Systems

Print ISBN: 978-3-319-32371-8

Electronic ISBN: 978-3-319-32372-5

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-32372-5_5