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Stabilizing and Optimizing Control for Time-Delay Systems

Including Model Predictive Controls


  • Introduces three important stabilizing controls in the time domain with unified frameworks and notations

  • Utilizes linear matrix inequalities in stabilizing and optimizing control designs for easier computation of complex controls

  • Supported by numerical examples with MATLAB codes for difficult optimal and sub-optimal stabilizing controls for time-delay systems

  • Provides the reader with coverage on both state- and input-delayed systems


Part of the Communications and Control Engineering book series (CCE)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Wook Hyun Kwon, PooGyeon Park
    Pages 1-26
  3. Wook Hyun Kwon, PooGyeon Park
    Pages 27-63
  4. Wook Hyun Kwon, PooGyeon Park
    Pages 65-93
  5. Wook Hyun Kwon, PooGyeon Park
    Pages 95-132
  6. Wook Hyun Kwon, PooGyeon Park
    Pages 133-185
  7. Wook Hyun Kwon, PooGyeon Park
    Pages 187-264
  8. Wook Hyun Kwon, PooGyeon Park
    Pages 265-318
  9. Wook Hyun Kwon, PooGyeon Park
    Pages 319-387
  10. Back Matter
    Pages 389-425

About this book


Stabilizing and Optimizing Control for Time-Delay Systems introduces three important classes of stabilizing controls for time-delay systems: non-optimal (without performance criteria); suboptimal (including guaranteed costs); and optimal controls. Each class is treated in detail and compared in terms of prior control structures. State- and input-delayed systems are considered. The book provides a unified mathematical framework with common notation being used throughout.

Receding-horizon, or model predictive, linear quadratic (LQ), linear-quadratic-Gaussian and H∞ controls for time-delay systems are chosen as optimal stabilizing controls. Cost monotonicity is investigated in order to guarantee the asymptotic stability of closed-loop systems operating with such controls.

The authors use guaranteed LQ and H∞ controls as representative sub-optimal methods; these are obtained with pre-determined control structures and certain upper bounds of performance criteria. Non-optimal stabilizing controls are obtained with predetermined control structures but with no performance criteria. Recently developed inequalities are exploited to obtain less conservative results.

To facilitate computation, the authors use linear matrix inequalities to represent gain matrices for non-optimal and sub-optimal stabilizing controls, and all the initial conditions of coupled differential Riccati equations of optimal stabilizing controls. Numerical examples are provided with MATLAB® codes (downloadable from to give readers guidance in working with more difficult optimal and suboptimal controls.

Academic researchers studying control of a variety of real processes in chemistry, biology, transportation, digital communication networks and mechanical systems that are subject to time delays will find the results presented in Stabilizing and Optimizing Control for Time-Delay Systems to be helpful in their work. Practitioners working in related sectors of industry will also find this book to be of use in developing real-world control systems for the many time-delayed processes they encounter.


Stability and Stabilization Non-Optimal Stabilizing Control Optimal Stabilizing Control Sub-Optimal Stabilizing Control Guaranteed Cost Control Robust Stabilizing Control LQ control LQG control H∞ control Receding Horizon Control Model Predictive Control Time-Delay Systems Reduction Transformation Finite Horizon Control Linear Matrix Inequality Integral Inequality Linear-Quadratic Control Linear-Quadratic-Gaussian Control

Authors and affiliations

  1. 1.Department of Electrical and Computer EngineeringSeoul National UniversitySeoulKorea (Republic of)
  2. 2.Department of Electrical EngineeringPOSTECHPohangKorea (Republic of)

About the authors

Wook Hyun Kwon received B.S. and M.S. degrees in electrical engineering from Seoul National University in 1966 and 1972, respectively, and a Ph D. degree from Brown University in 1975. He was an adjunct assistant professor at the University of lowa (1976-1977). He has been with Seoul National University since 1977, where he is currently a professor emeritus of School of Electrical and Computer Engineering since 2008. He was a visiting assistant professor at Stanford University in 1981-1982. He was a chair professor of DGIST (Daegu Gyeongbuk Institute of Science and Technology) in 2010-2014. Between 2005 and 2008 Professor Kwon served as President of the International Federation of Automatic Control.

PooGyeon Park received B.S. and M.S. degrees in electrical engineering from Seoul National University in 1988 and 1990, respectively, and a Ph D. degree from Stanford University in 1995. He has been with POSTECH (Pohang University of Science and Technology) since 1996, where he is currently a professor of Department of Electrical Engineering since 2005. 

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