Book excerpt: This book covers new aspects and frameworks of control, design, and optimization based on the TP model transformation and its various extensions. The author outlines the three main steps of polytopic and LMI based control design: 1) development of the qLPV state-space model, 2) generation of the polytopic model; and 3) application of LMI to derive controller and observer. He goes on to describe why literature has extensively studied LMI design, but has not focused much on the second step, in part because the generation and manipulation of the polytopic form was not tractable in many cases. The author then shows how the TP model transformation facilitates this second step and hence reveals new directions, leading to powerful design procedures and the formulation of new questions. The chapters of this book, and the complex dynamical control tasks which they cover, are organized so as to present and analyze the beneficial aspect of the family of approaches (control, design, and optimization). Additionally, the book aims to convey simple TP modeling; a new convex hull manipulation based possibilities for optimization; a general framework for stability analysis; standardized modeling and system description; relaxed and universal LMI based design framework; and a gateway to time-delayed systems.