### Optimization and Systems Theory Seminar

Friday, May 20, 2005, 11.00-12.00, Room 3721, Lindstedtsvägen 25

**Henrik Sandberg**

Department of Automatic Control

Lund Institute of Technology

Lund, Sweden

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Frequency-domain analysis of linear time-periodic systems

In this seminar, we discuss the construction of
frequency-response operators for linear time-periodic systems. These
operators have been useful for modeling of, for example, sampled-data
systems and switched power systems.
There are many different ways of constructing a frequency-response
operator. Here we use a Fourier expansion of the impulse response. It
turns out that it is then easy to perform so-called lifting in the
frequency domain. The result is an infinite-dimensional linear operator,
the Harmonic Transfer Function (HTF), that maps the frequency content in
the signals.

For computations, the HTF needs to be approximated with
finite-dimensional objects. To get explicit convergence bounds for
finite-dimensional projections, we can use generalized Taylor
expansions. We also show that once the convergence properties are
understood, it is relatively straightforward to generalize Bode's
sensitivity integral to the time-periodic case.

Calendar of seminars

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by Anders Forsgren.
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