A frequency domain analysis and synthesis of the passivity of sampled-data systems

We present a frequency-domain solution to the sampled-data passivity problem. Our analysis is exact in that we take into account the intersample behavior of the sampled-data system. We use frequency-response operators and derive a necessary and sufficient condition on the discrete controller that renders a passive closed-loop system. We then find a finite-dimensional system whose closed-loop passivity is equivalent to that of the original one, thus solving the sampled-data passivity synthesis problem. Computations of the equivalent system are carried out in the frequency domain.