The first part of the book deals with fractional derivative and fractional model definitions, as well as recent results for stability analysis, fractional model physical interpretation, controllability, and H-infinity norm computation. It also presents a critical point of view on model pseudo-state and "real state", tackling the problem of fractional model initialization.

Readers will find coverage of PID, Fractional PID and robust control in the second part of the book, which rounds off with an extension of H-infinity control to fractional models. An exhaustive description of the three generations of CRONE is also provided, along with several useful academic examples, treated with the CRONE control Matlab toolbox, which illustrate the various control strategies.

Since prefilters are additional but often under-studied degrees of freedom to tune a control loop, the last part of this book presents three different approaches: fractional prefilter, input shaping and flatness principles that have been extended to fractional models. All these approaches are applied to experimental closed loop systems.