The second edition of Generalized Homogeneity in Systems and Control is an introduction to the theory of homogeneous systems, useful for the simplification of many types of nonlinear control problem. It propounds methods that can be employed when linearization proves unsuitable and provides a unified approach to stability and robustness analysis, control and observer design, and system discretization.
The second edition splits the coverage of homogeneity, allowing expanded coverage of finite-dimensional systems (in Volume I) and infinite-dimensional systems (in this book). The results are better systematized and easier for readers to study and assimilate.
Generalized Homogeneity in Systems and Control Volume II (second edition) moves from stability analysis to the design of controllers for various systems. Key features of the book include:
- mathematical models of dynamical systems in infinite-dimensional spaces;
- the theory of linear dilations in Banach and Hilbert spaces (including Lebesgue and Sobolev spaces);
- abstract differential equations with homogeneous operators (including differential operators);
- rewritten, reorganized chapters with the addition of substantial new material;
- robustness analysis of infinite-dimensional homogeneous systems;
- homogeneous control in a Hilbert space; and
- consistent discretization of homogeneous systems.
Illustrative examples – numerical results, computer simulations and real experiments – support all the theoretical material. The coverage of infinite-dimensional systems presented in this book will be of interest to graduate students of control theory and applied mathematics and academic researchers in control.
Andrey Polyakov received his PhD in Systems Analysis and Control from the Voronezh State University, Russia in 2005. Until 2010 he was an associate professor with the same university. In 2007 and 2008, he was also a research associate with the CINVESTAV-IPN center in Mexico City. From 2010 up to 2013 he was a leader researcher of the Institute of the Control Sciences, Russian Academy of Sciences. In 2013 he joined Inria, Lille, France as a researcher. He hasco-authored more than 100 papers in peer-reviewed journals and three books Attractive Ellipsoids in Robust Control, Road Map for Sliding Mode Control Design and Generalized Homogeneity in Systems and Control 1st Ed. His research interests include various aspects of nonlinear control and estimation theory such as finite-time/fixed-time control, generalized homogeneity and Lyapunov methods for both finite-dimensional and infinite-dimensional systems.
