© 2018

Stability and Stabilization of Linear and Fuzzy Time-Delay Systems

A Linear Matrix Inequality Approach


Part of the Intelligent Systems Reference Library book series (ISRL, volume 141)

Table of contents

  1. Front Matter
    Pages i-xx
  2. Rajeeb Dey, Goshaidas Ray, Valentina Emilia Balas
    Pages 1-31
  3. Rajeeb Dey, Goshaidas Ray, Valentina Emilia Balas
    Pages 33-123
  4. Rajeeb Dey, Goshaidas Ray, Valentina Emilia Balas
    Pages 125-183
  5. Rajeeb Dey, Goshaidas Ray, Valentina Emilia Balas
    Pages 185-223
  6. Rajeeb Dey, Goshaidas Ray, Valentina Emilia Balas
    Pages 225-242
  7. Back Matter
    Pages 243-267

About this book


This book provides a clear understanding in formulating stability analysis and state feedback control of retarded time delay systems using Lyapunov’s second method in an LMI framework. The chapters offer a clear overview of the evolution of stability analysis in terms of the construction of a Lyapunov functional and use of the integral inequalities in order to reduce the gap of delay upper bound estimate compared to frequency domain method through existing and proposed stability theorems. Power system engineering problem has been presented here to give readers fair idea on applicability of the model and method for solving engineering problems. Without deviating from the framework of analysis more complex dynamics of the system have been dealt with here that includes actuator saturation and thereby ascertaining local stability for an estimated time-delay and domain of attraction. Nonlinearity in a time-delay system has been dealt with in the T-S fuzzy modeling approach.

This book is useful as a textbook for Master’s students and advanced researcher working in the field of control system engineering, and for practicing engineers dealing with such complex dynamical systems. The strengths of the book are lucidity of presentation, lucidity of solution method, MATLAB programs given in the appendix that help the novice researcher to carry out research in this area independently, clear idea about the formulation of desired stability and control problem in a LMI framework, application problem provided can motivate students and researcher to recast their problems in the similar framework easily, helpful for readers to use the stability (stabilization) conditions or formulate their own stability conditions easily for a complicated linear or nonlinear dynamical system.


Actuator Saturation Delay-dependent Criteria Domain of Attraction Fuzzy T-S Model H-infinity Control Intelligent Systems Linear Matrix Inequality (LMI) Lyapunov-Krasovskii Functional Stability and Stabilization Time-delay Systems Uncertain Systems

Authors and affiliations

  1. 1.National Institute of Technology SilcharSilcharIndia
  2. 2.Department of Electrical EngineeringIndian Institute of TechnologyKharagpurIndia
  3. 3.“Aurel Vlaicu” University of AradAradRomania

About the authors

Rajeeb Dey is presently working with National Institute of Technology, Silchar,
Assam, India, as Assistant Professor in the Department of Electrical Engineering.
Before joining NIT Silchar, he has served Sikkim Manipal University, Sikkim, for 12
years in various positions (Lecturer, Reader and Associate Professor). His research
interests are time-delay systems and control, robust control, control of biomedical
systems and application of wireless communication in control. He is presently
reviewer of many SCI(E) journals related to control engineering and applied math-
ematics. He is senior member of IEEE, CSS, Life member of System Society of India,
Member Institution of Engineers (India). E-mail:

Goshaidas Ray is presently full Professor in Heritage Institute of Technology,
Kolkata. Before joining Heritage Institute of Technology, he has served for over 35
years as a Professor in the Department of Electrical Engineering at Indian Institute
of Technology Kharagpur, India. He has published over 100 papers in reputed
international and national journals. E-mail:

Valentina Emilia Balas is currently full Professor in the Department of Automatics
and Applied Software at the Faculty of Engineering, “Aurel Vlaicu” University of
Arad, Romania. She holds a Ph.D. in Applied Electronics and Telecommunications
from Polytechnic University of Timisoara. Dr. Balas is author of more than 250
research papers in refereed journals and International Conferences. Her research
interests are in Intelligent Systems, Fuzzy Control, Soft Computing, Smart Sensors,
Information Fusion, Modeling and Simulation. She is the Editor-in Chief to
International Journal of Advanced Intelligence Paradigms (IJAIP) and to
International Journal of Computational Systems Engineering (IJCSysE), member
in Editorial Board member of several national and international journals and is the
director of Intelligent Systems Research Centre in Aurel Vlaicu University of Arad.
She is a member of EUSFLAT, SIAM and a Senior Member IEEE, member in TC –
Fuzzy Systems (IEEE CIS), member in TC – Emergent Technologies (IEEE CIS),
member in TC – Soft Computing (IEEE SMCS). E-mail:

Bibliographic information

  • Book Title Stability and Stabilization of Linear and Fuzzy Time-Delay Systems
  • Book Subtitle A Linear Matrix Inequality Approach
  • Authors Rajeeb Dey
    Goshaidas Ray
    Valentina Emilia Balas
  • Series Title Intelligent Systems Reference Library
  • Series Abbreviated Title Intel.Syst.Ref.Library
  • DOI
  • Copyright Information Springer International Publishing AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Engineering Engineering (R0)
  • Hardcover ISBN 978-3-319-70147-9
  • Softcover ISBN 978-3-319-88892-7
  • eBook ISBN 978-3-319-70149-3
  • Series ISSN 1868-4394
  • Series E-ISSN 1868-4408
  • Edition Number 1
  • Number of Pages XX, 267
  • Number of Illustrations 43 b/w illustrations, 0 illustrations in colour
  • Topics Computational Intelligence
    Artificial Intelligence
    Control and Systems Theory
  • Buy this book on publisher's site
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