Seminar Details
2007-03-20 (14pm) : "A lecture on homogeneity"
At Auditoire Euler
Organized by Mathematical Engineering
Speaker :
Tuna Emre (ULg)
Abstract :
Being a superclass of linear systems, homogenous systems can serve as better approximations to certain nonlinear systems. Their special
structure lets us study them locally to get a global idea. In this talk we give an overview of homogeneity and homogeneous systems with
emphasis on numerically realizable optimization schemes. Starting from the classical definition of dilations (and homogeneity with respect to
them), we take a natural path to generalization and obtain broader definitions which let us generalize previous results. Following that,
for a homogeneous discrete-time system, we consider an infinite horizon optimization problem (the solution of which is a control
Lyapunov function) and present a numerical algorithm to obtain a global solution. Later, we point our attention to switched systems.
We provide a method to generate a feedback law that stabilizes a homogeneous system under arbitrary switching. To the end, we talk
about the growth rate of a switched homogeneous system which is the analog of joint spectral radius of switched linear systems.