Squaring-Up Method for Relative Degree Two Plants

Non-square multi-input-multi-output (MIMO) plants are becoming increasingly common, as the addition of multiple sensors is becoming prevalent. However, square systems are needed sometimes as an leverage when it comes to design and analysis, as they possess desirable properties such as strict positive realness. This paper presents a squaring up method that adds artificial inputs to a class of MIMO plants with relative degree two and stable transmission zeros, where number of outputs exceeds number of inputs. The proposed method is able to produce a square plant that has stable transmission zeros and uniform/nonuniform relative degree, and is used to carry out adaptive control of this class of plants and shown to lead to satisfactory performance in a numerical study.