Nonlinear Control Systems Ii

This book incorporates recent advances in the design of feedback laws to the purpose of globally stabilizing nonlinear systems via state or output feedback. It is a continuation of the first volume by Alberto Isidori on Nonlinear Control Systems. Specifically this second volume will cover:

• Stability analysis of interconnected nonlinear systems. The notion of Input-to-State stability and its role in analysing stability of cascade-connected or feedback-connected systems. The notion of dissipativity and its consequences (passivity and "gain").

• Robust stabilization in the case of parametric uncertainties. The case of state feedback: global or semi-global stabilization. The case of output feedback: semi-global stabilization.

• Robust stabilization in the case of unstructured perturbations. Feedback design via the small-gain approach. Robust semi-global stabilization via output feedback.

• Methods for asymptotic tracking, disturbance rejection and model following. Global and semi-global analysis.

• Normal forms for multi-input multi-output nonlinear systems form a global point of view. Their role in feedback design.

Nonlinear Control Systems II is a continuation of the same author’s classic work Nonlinear Control Systems (978-3-540-19916-8). Including further advances in this increasingly important field of control theory, the second volume presents a self-contained and co-ordinated description of several design methods. In particular, the text takes advantage of the recent vigorous growth in such methods and concepts as input-to-state stability, the small-gain criterion and passivity via feedback to increase the reader’s ability to design effective feedback laws for nonlinear systems with model uncertainties. Among the most important features of this text are:

• stability analysis of interconnected nonlinear systems, including the notions of input-to-state stability and its role in analysing cascade-connected or feedback-connected systems and of dissipativity and its consequences;

• robust stabilization in cases with parametric uncertainties – the use of global, semi-global and practical semi-global stabilization and the design of state feedback and output feedback laws;

• robust stabilization in cases with unstructured perturbations including disturbance attenuation and almost disturbance decoupling;

• global stabilization using bounded controls;

• normal forms for multi-input, multi-output nonlinear systems from the global point of view and their role in feedback design.

The primary purpose of this book is as a reference for scientists, mathematicians and engineers working in the design of nonlinear control systems but it will also be of use as a text for graduate students studying control theory and nonlinear dynamical systems.

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.

In 1979, Alberto Isidori initiated a research program aimed at the extension of so-called "geometric theory" of multivariable linear systems, pioneered in the early 1970s by various authors,to linear systems. Linear algebra and linear geometric methods were replaced in nonlinear systems by the methods of differential geometry, whose usefulness in the study of controllability, observability, and minimality of nonlinear systems had been demonstrated in the early 70s. The main intuition of Isidori was to use differential geometric methods in the synthesis of feedback laws for nonlinear systems, more or less in the same way as linear geometric methods were used in the synthesis of feedback laws for linear systems. The result of this seminal work was the development of systematic methods addressing outstanding design problems like feedback linearization, noninteracting control, disturbance decoupling, and model matching.

From 1985 to 1990 Isidori's research concentrated on the development of the "nonlinear analogue" of the notion of the "zero" of a transfer function. Taking as a point of departure the "geometric" interpretation of this notion, the concept of nonlinear zero dynamics was introduced, studied, and applied. As a result, it was shown that most of the features of the notion of zeros of the transfer function of a linear system are actually manifestations of more general principles. Remarkable examples of application of this theory consisted in the study and the solution of the nonlinear equivalent of the so-called "servomechanism problem" of linear system theory and in the characterization of the conditions for feedback equivalence to a nonlinear passive system.

Since the 90s, Isidori has focused his research interests on problems of disturbance attenuation and robust stabilization of nonlinear systems.

Professional Activities

-President of the European Union Control Association (1995-1997).
-Member of the IFAC Council (1993-1996).

-President-elect of IFAC (three-year term to begin following IFAC World Congress in Seoul 2008)
-On the Editorial Board of: European Journal of Control (since 1995), Automatica (since 1990), IEEE Transactions on Automatic Control (since 1990), International Journal of Control (since 1990), International Journal of Robust and Nonlinear Control (since 1991), Journal of Mathematical Systems, Estimation and Control (since 1991), Mathematics of Control, Signals and Systems (1987-89), Applied Stochastic Models and Data Analysis (since 1985), Systems and Control Letters (1981-88).

Awards and Honors

-Georgio Quazza Medal of IFAC, for 'pionering and fundamental contributions to the theory of nonlinear control,'? 1996.
-Fellow of the Institute of Electrical and Electronic Engineers, for ?fundamental contributions to nonlinear control theory', 1987.
-Outstanding Paper Award for papers published on IEEE Transactions on Automatic Control, in 1981 and in 1990.
-Outstanding Paper Award a paper published on Automatica in1991.

Selected Publications

Nonlinear Control Systems (3rd edition), Springer Verlag (1995), pp. 1-549.

Topics in Control Theory, with W. Knobloch and D. Flockerzi, Berkhauser (1993), pp. 1-166.

Output Regulation of Uncertain Nonlinear Systems, with C.I. Byrnes and F. Delli Priscoli, Birkhauser (1997), pp. 1-122.

Trends in Control Theory (editor), Springer Verlag (1995), pp. 1-422.

Systems, Models and Feedback (co-editor, with T.J. Tarn), Birkhauser (1992), pp. 1-402.