Generalized Dilations and Homogeneity

Within dynamical systems theory, homogeneity (ofsystems) has previously been defined with respect toa class of functions named dilations. This booktreats homogeneity in a more general way byextending the classical definition through a broaderclass of functions, named generalized dilations. Thenew way of looking at homogeneity yields thefollowing implications which constitute the most ofthe material studied in the book. Generalizeddilations make possible to devise optimization-basednumerical algorithms to obtain offline-computed,globally stabilizing feedback laws for a generalclass of discrete-time systems. Also, by nonstandardsample-and-hold techniques (which take homogeneityinto account) such algorithms tailored for discrete-time systems find applications in regulation ofcontinuous-time systems and even in stabilization ofswitched systems.

Autorentext

The author was born in 1979, in Iskenderun, Turkey. He received a Ph.D. degree in electrical and computer engineering from University of California, Santa Barbara, in 2005. He is currently an assistant professor at Middle East Technical University, Ankara.