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 expands the coverage of finite- and infinite-dimensional systems in this two-volume set (also available as separate volumes). The results are better systematized and easier for readers to study and assimilate.

Generalized Homogeneity in Systems and Control (second edition) includes the following key features:

• mathematical models of dynamical systems;
• the theory of linear dilations in Euclidean, Banach and Hilbert spaces (including Lebesgue and Sobolev spaces);
• homogeneous control and estimation;
• simple methods for an upgrade of existing control laws;
• numerical schemes for a consistent digital implementation of homogeneous algorithms;
• experimental results that confirm an improvement of PID controllers;
• abstract differential equations with homogeneous operators (including differential operators);
• rewritten, reorganized and original 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 finite- and infinite-dimensional systems presented in this set will be of interest to graduate students and academic researchers in control theory from engineering and applied-mathematical backgrounds and to practising control engineers.

Two-volume set provides a thorough introduction to the theory of generalized homogeneous systems Explains homogeneous control in a Hilbert space Supports all theory with illustrations, examples, and simulations

Autorentext

Andrey Polyakov received his Ph.D. in Systems Analysis and Control from the Voronezh State University, Russia in 2005. Until 2010, he was an associate professor at 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 at the Institute of the Control Sciences, Russian Academy of Sciences. In 2013, he joined Inria, Lille, France, as a researcher. He has co-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.