The linear least squares synthesis of multivariable control systems

A MULTIVARIABLE system is characterized by a multiplicity of inputs and outputs. In the following, it will be assumed that such systems can be described by linear, time-in variant, input-output relations over the whole range of operation or over the restricted range of interest. Thus, let then, the system input-output relation may be expressed compactly as where R, C, and A are input, output, and transfer-function matrices respectively; see Fig. 1. It is seen that a multivariable system derives each output by a simultaneous operation on all its inputs. Furthermore, it is apparent that the class of multivariable systems includes the common single-variable system as a special case.