Henrik Sandberg
Department of Automatic Control
Lund Institute of Technology
Lund, Sweden
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.
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