Nonlinear Control Systems II

10. Stability of Interconnected Nonlinear Systems.- 10.1 Preliminaries.- 10.2 Asymptotic Stability and Small Perturbations.- 10.3 Asymptotic Stability of Cascade-Connected Systems.- 10.4 Input-to-State Stability.- 10.5 Input-to-State Stability of Cascade-Connected Systems.- 10.6 The "Small-Gain" Theorem for Input-to-State Stable Systems.- 10.7 Dissipative Systems.- 10.8 Stability of Interconnected Dissipative Systems.- 10.9 Dissipative Linear Systems.- 11. Feedback Design for Robust Global Stability.- 11.1 Preliminaries.- 11.2 Stabilization via Partial State Feedback: a Special Case.- 11.3 Stabilization via Output Feedback: a Special Case.- 11.4 Stabilization of Systems in Lower Triangular Form.- 11.5 Design for Multi-Input Systems.- 12. Feedback Design for Robust Semiglobal Stability.- 12.1 Achieving Semiglobal and Practical Stability.- 12.2 Semiglobal Stabilization via Partial State Feedback.- 12.3 A Proof of Theorem 9.6.2.- 12.4 Stabilization of Minimum-Phase Systems in Lower-Triangular Form.- 12.5 Stabilization via Output Feedback Without a Separation Principle.- 12.6 Stabilization via Output Feedback of Non-Minimum-Phase Systems.- 12.7 Examples.- 13. Disturbance Attenuation.- 13.1 Robust Stability via Disturbance Attenuation.- 13.2 The Case of Linear Systems.- 13.3 Disturbance Attenuation.- 13.4 Almost Disturbance Decoupling.- 13.5 An Estimate of the Minimal Level of Disturbance Attenuation.- 13.6L2-gain Design for Linear Systems.- 13.7 GlobalL2-gain Design for a Class of Nonlinear Systems.- 14. Stabilization Using Small Inputs.- 14.1 Achieving Global Stability via Small Inputs.- 14.2 Stabilization of Systems in Upper Triangular Form.- 14.3 Stabilization Using Saturation Functions.- 14.4 Applications and Extensions.- Bibliographical Notes.- References.

Alberto Isidori was born in Rapallo, Italy. He graduated in electrical engineering from the University of Rome in 1965. In 1969 he obtained a degree equivalent to a doctorate in automatic control from the University of Rome.

Since 1975, he has been Professor of Automatic Control at the University of Rome "La Sapienza". Since 1989, he has also held a position of rofessor (on a half-time basis) at the Department of Systems Science and Mathematics, Washington University, St. Louis, Missouri. He has held visiting positions at several academic institutions, including the University of Illinois (Urbana, Il.), the University of California (Berkeley, Ca.) and the ETH (Zurich, Switzerland).

His research interests are primarily focused on mathematical control theory and control engineering.

From the reviews:

According to the Preface: "The purpose of this book is to present a self-contained and coordinated description of several design methods for nonlinear systems, with special emphasis on the problem of achieving stability, globally or on arbitrarily large domains, in the presence of model uncertainties. The book is intended to be a continuation of my earlier book [Nonlinear Control Systems, third edition, Springer, London, 1995]."

This statement provides an indication of the author's motivation and the emphasis of the presentation. The book provides a careful and detailed treatment of the selected topics.

It should be mentioned that intimate knowledge of Isidori's earlier book is not a prerequisite for the current book. Some references are made to the earlier book, but only relatively simple notions of relative degree and feedback transformations are used. Although the numbering scheme of the current book indicates a continuation of the earlier book, the topics covered are distinct and the two books can be studied independently.

Chapter 10 (the first chapter of the book) is devoted to the stability analysis of systems that can be viewed as a cascade or feedback interconnection. Basic analysis tools are introduced, including input-to-state stability, small gain theorem, dissipativity and passivity. Chapter 11 describes methods for global robust stabilization of nonlinear systems. Systems modelled by equations in lower-triangular form containing unknown parameters are introduced. Several control design approaches, based on different assumptions, are developed. Chapter 12 is concerned with "semi-global practical stabilizability". The case of output feedback is given considerable attention. In Chapter 13, the small-gain theorem is used to study robust stabilization in the presence of unmodeled dynamics. This leads to nonlinear H-infinity problems. Chapter 15 treats problems of stabilizability subject tocontrol