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

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
by Anders Forsgren.