skip to main content
10.1145/3459104.3459128acmotherconferencesArticle/Chapter ViewAbstractPublication PagesiseeieConference Proceedingsconference-collections
research-article

Derivative-based Fuzzy Control Synthesis for Singular Takagi-Sugeno Fuzzy Systems with Perturbations

Published: 20 July 2021 Publication History

Abstract

This paper focuses on stabilization issues for the nonlinear singular systems with internal perturbations. A novel robust fuzzy control technique is investigated based on the state-derivative feedback approach. In this paper, the nonlinear perturbed singular systems are expressed by the uncertain Takagi-Sugeno fuzzy models. The so-called parallel distributed compensation method is applied to design the state-derivative feedback fuzzy controller. Considering the Takagi-Sugeno fuzzy perturbed singular systems, the Lyapunov stability theory is employed to derive sufficient stability conditions with decay rate. Then transform these stability conditions into a linear matrix inequality problem. In the end, a numerical example is provided to verify the applicability of the proposed robust fuzzy controller design method.

References

[1]
G. Verghese, B. Lévy and T. Kailath, “A generalized state-space for singular systems”, IEEE Transactions on Automatic Control, Vol. 26, No. 4, pp. 811-831, 1981.
[2]
F. L. Lewis, “A survey of linear singular systems”, Circuits, systems and signal processing, Vol. 5, No, 1, pp. 3-36, 1986.
[3]
Z. Feng, J. Lam, S. Xu and S. Zhou, “H∞ control with transients for singular systems”, Asian Journal of Control, Vol. 18, No. 3, pp. 817-827, 2016
[4]
C. Han, Z. Yi and Z. Y. Zhao, “Admissibility analysis for nonlinear singular system with time-delay via T-S fuzzy model”, International Journal of Fuzzy Systems, Vol. 19, No. 1, pp. 207-214, 2015.
[5]
X. Fan, Q. Zhang and J. Ren, “Event-triggered sliding mode control for discrete-time singular system”, IET Control Theory and Applications, Vol. 12, No. 17, pp. 2390-2398, 2018.
[6]
S. Peng, H. Wang and C. C. Lim, “Network-based event-triggered control for singular systems with quantizations”, IEEE Transactions on Industrial Electronics, Vol. 63, No. 2, pp. 1230-1238, 2015.
[7]
W. J. Chang and B. J. Huang, “Robust fuzzy control subject to state variance and passivity constraints for perturbed nonlinear systems with multiplicative noises”, ISA Transactions, Vol. 53, No. 6, pp. 1787-1795, 2014
[8]
H. O. Wang, K. Tanaka and M. F. Griffin, “An approach to fuzzy control of nonlinear systems: Stability and design issues”, IEEE transactions on fuzzy systems, Vol. 4, No. 1, pp. 14-23, 1996.
[9]
K. Tanaka and H. O. Wang, Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach, John Wiley and Sons, Inc., New York, 2001.
[10]
W. J. Chang, C. C. Ku and C. H. Chang, “PDC and Non-PDC fuzzy control with relaxed stability conditions for continuous-time multiplicative noised fuzzy systems”, Journal of the Franklin Institute - Engineering and Applied Mathematics, Vol. 349, No. 8, pp. 2664-2686, 2012.
[11]
W. J. Chang, Y. H. Lin, J. Du and C. M. Chang, “Fuzzy control with pole assignment and variance constraints for continuous-time perturbed Takagi-Sugeno fuzzy models: Application to ship steering systems”, International Journal of Control, Automation and Systems, Vol. 17, No. 10, pp. 2677-2692, 2019.
[12]
W. J. Chang, C. P. Kuo and C. C. Ku, “Intelligent fuzzy control with imperfect premise matching concept for complex nonlinear multiplicative noised systems”, Neurocomputing, Vol. 154, pp. 276-283, 2015.
[13]
G. Zheng, D. Efimov, F. J. Bejarano and W. Perruquetti, “Robust stabilization for uncertain T–S fuzzy singular system”, International Journal of Machine Learning and Cybernetics, Vol. 7, No. 5, pp. 699-706, 2016.
[14]
H. Yueqiao, Y. Kao, and C. Gao, “Robust sliding mode control for uncertain discrete singular systems with time-varying delays and external disturbances”, Automatica, Vol. 75, pp. 210-216, 2017.
[15]
T. Insperger, J. Milton and G. Stépán, “Acceleration feedback improves balancing against reflex delay”, Journal of the Royal Society Interface, Vol. 10, No, 79, 2013.
[16]
E. M. C. Barbosa, de Oliveira Souza Fernando and M. P. Reinaldo, “LMI-based Design of State-Derivative Feedback Control for Takagi-Sugeno Fuzzy Descriptor Systems,” SBAI 2019, Vol. 1, 2019.
[17]
R. Zaghdoud, S. Salah and K. Moufida, “State derivative feedback for singular systems,” IMA Journal of Mathematical Control and Information, Vol. 35, No. 2, pp. 611-626, 2018.
[18]
A. Haraldsdottir, P. T. Kabamba and A. G. Ulsoy, “Sensitivity reduction by state derivative feedback,” Journal of Dynamic Systems, Measurement, and Control, Vol. 110, No. 1, pp. 83-94, 1988.
[19]
A. B. Gerstner, V. Mehrmann and N. K. Nichols, “Regularization of descriptor systems by derivative and proportional state feedback,” SIAM Journal on Matrix Analysis and Applications, Vol. 13, No. 1, pp. 46–67, 1992.
[20]
E. Assunção, M. C. M. Teixeira, F. A. Faria, “Robust state-derivative feedback LMI-based designs for multivariable linear systems,” International Journal of Control, Vol. 80, No. 8, pp.1260-1270, 2007.
[21]
W. J. Chang, C. C. Ku, and P. H. Huang, “Robust fuzzy control for uncertain stochastic time-delay Takagi-Sugeno fuzzy models for achieving passivity,” Fuzzy Sets and Systems, Vol. 161, No. 15, pp. 2012-2032, 2010.
[22]
S. Boyd, L. E. Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, 1994.

Cited By

View all
  • (2021)Observer-Based Fuzzy Controller Design for Nonlinear Discrete-Time Singular Systems via Proportional Derivative Feedback SchemeApplied Sciences10.3390/app1106283311:6(2833)Online publication date: 22-Mar-2021

Index Terms

  1. Derivative-based Fuzzy Control Synthesis for Singular Takagi-Sugeno Fuzzy Systems with Perturbations
          Index terms have been assigned to the content through auto-classification.

          Recommendations

          Comments

          Information & Contributors

          Information

          Published In

          cover image ACM Other conferences
          ISEEIE 2021: 2021 International Symposium on Electrical, Electronics and Information Engineering
          February 2021
          644 pages
          ISBN:9781450389839
          DOI:10.1145/3459104
          Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

          Publisher

          Association for Computing Machinery

          New York, NY, United States

          Publication History

          Published: 20 July 2021

          Permissions

          Request permissions for this article.

          Check for updates

          Author Tags

          1. Derivative Feedback
          2. Robust Control
          3. Singular systems
          4. Takagi-Sugeno Fuzzy Systems

          Qualifiers

          • Research-article
          • Research
          • Refereed limited

          Funding Sources

          • National Science Council of the Republic of China

          Conference

          ISEEIE 2021

          Contributors

          Other Metrics

          Bibliometrics & Citations

          Bibliometrics

          Article Metrics

          • Downloads (Last 12 months)3
          • Downloads (Last 6 weeks)0
          Reflects downloads up to 19 Feb 2025

          Other Metrics

          Citations

          Cited By

          View all
          • (2021)Observer-Based Fuzzy Controller Design for Nonlinear Discrete-Time Singular Systems via Proportional Derivative Feedback SchemeApplied Sciences10.3390/app1106283311:6(2833)Online publication date: 22-Mar-2021

          View Options

          Login options

          View options

          PDF

          View or Download as a PDF file.

          PDF

          eReader

          View online with eReader.

          eReader

          HTML Format

          View this article in HTML Format.

          HTML Format

          Figures

          Tables

          Media

          Share

          Share

          Share this Publication link

          Share on social media