Optimal and Robust Control: Advanced Topics with MATLAB®, 1st Edition (Hardback) book cover

Optimal and Robust Control

Advanced Topics with MATLAB®, 1st Edition

Edited by Luigi Fortuna, Mattia Frasca

CRC Press

251 pages | 62 B/W Illus.

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While there are many books on advanced control for specialists, there are few that present these topics for nonspecialists. Assuming only a basic knowledge of automatic control and signals and systems, Optimal and Robust Control: Advanced Topics with MATLAB® offers a straightforward, self-contained handbook of advanced topics and tools in automatic control.

Techniques for Controlling System Performance in the Presence of Uncertainty

The book deals with advanced automatic control techniques, paying particular attention to robustness—the ability to guarantee stability in the presence of uncertainty. It explains advanced techniques for handling uncertainty and optimizing the control loop. It also details analytical strategies for obtaining reduced order models. The authors then propose using the Linear Matrix Inequalities (LMI) technique as a unifying tool to solve many types of advanced control problems.

Topics covered include:

  • LQR and H-infinity approaches
  • Kalman and singular value decomposition
  • Open-loop balancing and reduced order models
  • Closed-loop balancing
  • Passive systems and bounded-real systems
  • Criteria for stability control

This easy-to-read text presents the essential theoretical background and provides numerous examples and MATLAB exercises to help the reader efficiently acquire new skills. Written for electrical, electronic, computer science, space, and automation engineers interested in automatic control, this book can also be used for self-study or for a one-semester course in robust control.


"This textbook deals with advanced topics from optimal and robust control and presents these topics in particular for non specialists. … The book is well-written and provides a self-contained overview about advanced topics in optimal and robust control. It is in particular written for electrical, electronic, computer science, space and automatic engineers interested in automatic control."

—Birgit Jacob (Wuppertal), Zentralblatt MATH, 1248 — 1

Table of Contents

Modelling of uncertain systems and the robust control problem

Uncertainty and robust control

The essential chronology of major findings into robust control

Fundamentals of stability

Lyapunov criteria

Positive definite matrices

Lyapunov theory for linear time-invariant systems

Lyapunov equations

Stability with uncertainty


Kalman canonical decomposition


Controllability canonical partitioning

Observability canonical partitioning

General partitioning

Remarks on Kalman decomposition


Singular value decomposition

Singular values of a matrix

Spectral norm and condition number of a matrix


Open-loop balanced realization

Controllability and observability gramians

Principal component analysis

Principal component analysis applied to linear systems

State transformations of gramians

Singular values of linear time-invariant systems

Computing the open-loop balanced realization

Balanced realization for discrete-time linear systems


Reduced order models

Reduced order models based on the open-loop balanced realization

Reduced order model exercises


Symmetrical systems

Reduced order models for SISO systems

Properties of symmetrical systems

The cross-gramian matrix

Relations between W2c , W2o and Wco

Open-loop parameterization

Relation between the Cauchy index and the Hankel matrix

Singular values for a FIR filter

Singular values of all-pass systems


Linear quadratic optimal control

LQR optimal control

Hamiltonian matrices

Resolving the Riccati equation by Hamiltonian matrix

The Control Algebraic Riccati Equation

Optimal control for SISO systems

Linear quadratic regulator with cross-weighted cost

Finite-horizon linear quadratic regulator

Optimal control for discrete-time linear systems


Closed-loop balanced realization

Filtering Algebraic Riccati Equation

Computing the closed-loop balanced realization

Procedure for closed-loop balanced realization

Reduced order models based on closed-loop balanced realization

Closed-loop balanced realization for symmetrical systems


Passive and bounded-real systems

Passive systems

Circuit implementation of positive-real systems

Bounded-real systems

Relationship between passive and bounded-real systems


H∞ linear control


Solution of the H∞ linear control problem

The H∞ linear control and the uncertainty problem


Linear Matrix Inequalities for optimal and robust control

Definition and properties of LMI

LMI problems

Formulation of control problems in LMI terms

Solving a LMI problem

LMI problem for simultaneous stabilizability

Solving algebraic Riccati equations through LMI

Computation of gramians through LMI

Computation of the Hankel norm through LMI

H∞ control

Multiobjective control


The class of stabilizing controllers

Parameterization of stabilizing controllers for stable processes

Parameterization of stabilizing controllers for unstable processes

Parameterization of stable controllers

Simultaneous stabilizability of two systems

Coprime factorizations for MIMO systems and unitary factorization

Parameterization in presence of uncertainty


Recommended essential references

Appendix A. Norms

Appendix B. Algebraic Riccati Equations


About the Editors

Luigi Fortuna is a Full Professor of System Theory at the University of Catania, Italy. He was the coordinator of the courses in electronic engineering and Head of the Dipartimento di Ingegneria Elettrica Elettronica e dei Sistemi (DIEES). Since 2005, he has been the Dean of the Engineering Faculty. He currently teaches complex adaptive systems and robust control. He has published more than 450 technical papers and is the coauthor of ten scientific books. His scientific interests include robust control, nonlinear science and complexity, chaos, cellular neural networks, soft-computing strategies for control and robotics, micronanosensor and smart devices for control, and nanocellular neural networks modeling. Dr. Fortuna is an IEEE Fellow.

Mattia Frasca received his PhD in Electronics and Automation Engineering in 2003, at the University of Catania, Italy. Currently, he is a research associate at the University of Catania, where he also teaches systems theory. His scientific interests include robust control, nonlinear systems and chaos, cellular neural networks, complex systems, and bio-inspired robotics. He is involved in many research projects and collaborations with industries and academic centers. He is also a referee for many international journals and conferences. Dr. Frasca was on the organizing committee of the 10th Experimental Chaos Conference and was co-chair of the 4th International Conference on Physics and Control. He is the coauthor of three research monographs, has published more than 150 papers in refereed international journals and international conference proceedings, and is the coauthor of two international patents. He is also a Senior Member of IEEE.

For more information on Dr. Frasca’s work, see his web page at the University of Catania.

Subject Categories

BISAC Subject Codes/Headings:
TECHNOLOGY & ENGINEERING / Electronics / Microelectronics