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.

• Chapter 1. Introduction to Abstract Homogeneity.- Chapter 2. Abstract Differential Equations.- Chapter 3. Lyapunov Methods for Abstract Differential Equations.- Chapter 4. Linear Dilations in Abstract Spaces.- Chapter 5. Infinite-Dimensional Homogeneous Mappings.- Chapter 6. Analysis of Infinite-Dimensional Homogeneous Systems.- Chapter 7. Discretization of Infinite-Dimensional Homogeneous Systems.- Chapter 8. Homogeneous Stabilization of Infinite-Dimensional Systems.

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.

• Chapter 1. Introduction to Abstract Homogeneity.- Chapter 2. Abstract Differential Equations.- Chapter 3. Lyapunov Methods for Abstract Differential Equations.- Chapter 4. Linear Dilations in Abstract Spaces.- Chapter 5. Infinite-Dimensional Homogeneous Mappings.- Chapter 6. Analysis of Infinite-Dimensional Homogeneous Systems.- Chapter 7. Discretization of Infinite-Dimensional Homogeneous Systems.- Chapter 8. Homogeneous Stabilization of Infinite-Dimensional Systems.

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.

• Chapter 1. Introduction to Abstract Homogeneity.- Chapter 2. Abstract Differential Equations.- Chapter 3. Lyapunov Methods for Abstract Differential Equations.- Chapter 4. Linear Dilations in Abstract Spaces.- Chapter 5. Infinite-Dimensional Homogeneous Mappings.- Chapter 6. Analysis of Infinite-Dimensional Homogeneous Systems.- Chapter 7. Discretization of Infinite-Dimensional Homogeneous Systems.- Chapter 8. Homogeneous Stabilization of Infinite-Dimensional Systems.