Within dynamical systems theory, homogeneity (of systems) has previously been defined with respect to a class of functions named dilations. This book treats homogeneity in a more general way by extending the classical definition through a broader class of functions, named generalized dilations. The new way of looking at homogeneity yields the following implications which constitute the most of the material studied in the book. Generalized dilations make possible to devise optimization-based numerical algorithms to obtain offline-computed, globally stabilizing feedback laws for a general class of discrete-time systems. Also, by nonstandard sample-and-hold techniques (which take homogeneity into account) such algorithms tailored for discrete- time systems find applications in regulation of continuous-time systems and even in stabilization of switched systems.

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