Lectures in Feedback Design for Multivariable Systems

  • Alberto Isidori

Table of contents

  1. Front Matter
    Pages i-xi
  2. Alberto Isidori
    Pages 1-18
  3. Linear Systems

  4. Nonlinear Systems

  5. Back Matter
    Pages 365-413

About this book


This book focuses on methods that relate, in one form or another, to the “small-gain theorem”. It is aimed at readers who are interested in learning methods for the design of feedback laws for linear and nonlinear multivariable systems in the presence of model uncertainties. With worked examples throughout, it includes both introductory material and   more advanced topics.

Divided into two parts, the first covers relevant aspects of linear-systems theory, the second, nonlinear theory. In order to deepen readers’ understanding, simpler single-input–single-output systems generally precede treatment of more complex multi-input–multi-output (MIMO) systems and linear systems precede nonlinear systems. This approach is used throughout, including in the final chapters, which explain the latest advanced ideas governing the stabilization, regulation, and tracking of nonlinear MIMO systems. Two major design problems are considered, both in the presence of model uncertainties: asymptotic stabilization with a “guaranteed region of attraction” of a given equilibrium point and asymptotic rejection of the effect of exogenous (disturbance) inputs on selected regulated outputs.

Much of the introductory instructional material in this book has been developed for teaching students, while the final coverage of nonlinear MIMO systems offers readers a first coordinated treatment of completely novel results. The worked examples presented provide the instructor with ready-to-use material to help students to understand the mathematical theory.

Readers should be familiar with the fundamentals of linear-systems and control theory. This book is a valuable resource for students following postgraduate programs in systems and control, as well as engineers working on the control of robotic, mechatronic and power systems.


Advanced Control Theory Methods for Robust Control Control of Nonlinear Systems Control of Linear Systems Robust Stabilization Small-gain Theorem Control of Multivariable Ssytems Regulation of Nonlinear Systems Tracking Control Regulation of Linear Systems

Authors and affiliations

  • Alberto Isidori
    • 1
  1. 1.Dipartimento di Ingegneria Informatica, Automatica e Gestionale"Sapienza" Universita di RomaRomaItaly

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing Switzerland 2017
  • Publisher Name Springer, Cham
  • eBook Packages Engineering Engineering (R0)
  • Print ISBN 978-3-319-42030-1
  • Online ISBN 978-3-319-42031-8
  • Series Print ISSN 1439-2232
  • Buy this book on publisher's site