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The Center for Control, Dynamical Systems, and Computation Spring Seminars

Summary: The Center for Control, Dynamical Systems, and Computation
Spring Seminars
Frequency-Domain Analysis of Linear
Time-Periodic Systems
Professor Henrik Sandberg
Institute for Mathematics
University of Caltech
Friday, April 21st, 2006 3:00 - 4:00 PM Engineering II Pavilion
In this seminar, we discuss the construction of a frequency-response operator for linear time-periodic
systems. The particular operator we obtain has been useful for modeling of sampled-data systems and power
systems. Furthermore, the operator has an appealing visualization that shows the coupling between different
To construct the frequency-response operator, we use a Fourier expansion of the impulse response, followed
by so-called lifting in the frequency domain. The result is an infinite-dimensional 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


Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara


Collections: Mathematics