On minimal-order stabilization of minimum phase plants

In this note, the problem of minimal-order stabilization in the case where the plant is minimum phase is studied. A low bound on the order of stabilizers is derived and a set of minimal-order stabilizers are characterized. The low bound is related to the number and location of the plant's unstable and lightly damped poles and the number of zeros. How to construct a minimal-order or low-order stabilizer for a general case is also discussed and the algorithm is provided. Numerical examples are given to illustrate the proposed method.