Optimization and Systems Theory Seminar
Friday March 26, 2010, 11.00-12.00, Room 3721, Lindstedtsvägen 25
Elias Jarlebring
K.U. Leuven, Belgium
Computational methods for the H2 norm and the characteristic roots of
time-delay systems
The transfer function can be used in a number of ways to analyze
dynamical systems. If the state equation of a continuous-time linear
time-invariant (LTI) system has a delayed term, then the transfer
function will contain a corresponding exponential term. In this talk
we will present two results on LTI systems with delays, here called
time-delay systems.
We present methods to compute the H2-norm of the transfer
function of a time-delay system. The H2-norm of LTI systems without
delay can be computed from the solution of the Lyapunov equation. We
show that this extends to systems with delays, where instead, the
so-called delay Lyapunov equation has to be solved. It turns out that
the delay Lyapunov equation can be solved explicitly for time-delay
systems with a single delay and we propose a new numerical scheme for
the general case.
The method called Arnoldi is a very popular method for standard
eigenvalue problems. Because of the exponential term in the
denominator of the transfer function of time-delay systems, the
characteristic equation is a nonlinear eigenvalue problem. We also
present a natural generalization of Arnoldi for this nonlinear
eigenvalue problem. The generalization is done in such a way that
many attractive properties of Arnoldi are preserved. In particular the
method is such that an arbitrary number of characteristic roots can be
computed efficiently in a robust way.
Calendar of seminars
Last update: February 10, 2010.