For nonlinear dynamical systems, which represent the majority of real devices, any study of stability requires the investigation of the domain of attraction of an equilibrium point, i.e. the set of initial conditions from which the trajectory of the system converges to equilibrium. Unfortunately, both estimating and attempting to control the domain of attraction are very difficult problems, because of the complex relationship of this set with the model of the system. Domain of Attraction addresses the estimation and control of the domain of attraction of equilibrium points via SOS programming, i.e. optimization techniques based on the sum of squares of polynomials (SOS) that have been recently developed and that amount to solving convex problems with linear matrix inequality constraints. A unified framework for addressing these issues is presented for in various cases depending on the nature of the nonlinear systems considered, including the cases of polynomial, non-polynomial, certain and uncertain systems. The methods proposed are illustrated various example systems such as electric circuits, mechanical devices, and nuclear plants. Domain of Attraction also deals with related problems that can be considered within the proposed framework, such as characterizing the equilibrium points and bounding the trajectories of nonlinear systems, and offers a concise and simple description of the main features of SOS programming, which can be used for general purpose in research and teaching.

Robots able to imitate human beings have been at the core of stories of science?ctionaswellasdreamsofinventorsforalongtime.Amongthe various skills that Mother Nature has provided us with and that often go forgotten, the ability of sight is certainly one of the most important. Perhaps inspired by tales of Isaac Asimov, comics and cartoons, and surely helped by the progress of electronics in recent decades, researchers have progressively made the dream of creating robots able to move and operate by exploiting arti?cial vision a concrete reality. Technically speaking, we would say that these robots position themselves and their end-e?ectors by using the view provided by some arti?cial eyes as feedback information. Indeed, the arti?cial eyes are visual sensors such as cameras that have the function to acquire an image of the environment. Such an image describes if and how the robot is moving toward the goal and hence constitutes feedback information. This procedure is known in robotics with the term visual servoing, and it is nothing else than an imitation of the intrinsic mechanism that allows human beings to realize daily tasks such as reaching the door of the house or grasping a cup of co?ee.

It is well known that a large number of problems relevant to the control ?eld can be formulatedas optimizationproblems. For long time, the classical approachhas been to look for a closed form solution to the speci?c optimizationproblems at hand. The last decade has seen a noticeable shift in the meaning of "closed form" solution. The formidable increase of computationalpower has dramatically changed the fe- ing of theoreticians as well as of practitioners about what is meant by tractable and untractableproblems. A main issue regardsconvexity. From a theoretical viewpoint, there has been a large amount of work in the directions of "convexifying" nonc- vex problems and studying structural features of convex problems. On the other hand, extremely powerful algorithmsfor the solution of convexproblemshave been devised in the last two decades. Clearly, the fact that a wide variety of engine- ing problems can be formulated as convex problems has strongly motivated efforts in this direction. The control ?eld is not an exception in this sense: many pr- lems in robust control, identi?cation and nonlinear control have been recognized as convex problems. Moreover, convex relaxations of nonconvex problems have been intensively investigated, as they provide an effective tool for bounding the optimal solution of the original problem. As far as robust control is concerned, it is known since long time that several classes of problemscan be reducedto testing positivity of suitable polynomials.