 
Summary: The Center for Control, Dynamical Systems, and Computation
Spring Seminars
Presents
FrequencyDomain Analysis of Linear
TimePeriodic Systems
by
Professor Henrik Sandberg
Institute for Mathematics
University of Caltech
Friday, April 21st, 2006 3:00  4:00 PM Engineering II Pavilion
Abstract:
In this seminar, we discuss the construction of a frequencyresponse operator for linear timeperiodic
systems. The particular operator we obtain has been useful for modeling of sampleddata systems and power
systems. Furthermore, the operator has an appealing visualization that shows the coupling between different
frequencies.
To construct the frequencyresponse operator, we use a Fourier expansion of the impulse response, followed
by socalled lifting in the frequency domain. The result is an infinitedimensional linear operator, often called the
harmonic transfer function (HTF), that maps the frequency content of the input signal into the output signal.
To use the HTF for computations, it needs to be approximated by finite mappings. To get approximation error
bounds, we use generalized Taylor expansions. These give bounds on the modulus of the elements in the
