Squaring-down and the problems of almost-zeros for continuous-time systems

In this paper we construct precompensators which square-down a system such that the resulting square system has the same unstable zeros and system gains. We derive the minimal gain of the precompensator to achieve such a square system. If the gain of this precompensator is too large then we derive an explicit trade-off between the gain of the precompensator and the number of unstable zeros we allow the precompensator to introduce in the system. Keywords: Nehari approximation, Almost-zeros, Squaring-down.