Stability of zeros of sampled MIMO systems with GSHF

It is well-known that unstable zeros limit the achievable control performance and generalized sampled hold function can be used to shift the zeros of sampled-data models for continuous-time systems. This paper analyzes the the stability of the limiting zeros of the discrete-time MIMO systems composed of a generalized sample hold function (GSHF), a continuous-time plant with the degrees of infinite elementary divisors being two or three, and a samples in cascade. The conditions that ensure the stability of the limiting zeros of discrete-time systems for sufficiently small sampling periods are derived and proof in detail.