The synthesis of linear multivariable systems by state-variable feedback

Design procedures are presented for the compensation of linear multivariable-feedback systems. The design objectives which are noninteraction and low-order compensators are obtained by state-variable feedback. A <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</tex> th order plant with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</tex> inputs and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</tex> outputs where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q&gt;m</tex> is treated. All the state variables are assumed to be available and measurable. It is shown that it is often possible by state-variable feedback to obtain noninteraction without an increase in system order. When the determinant of the plant transfer-function matrix has right half plane zeros the state-variable feedback method cannot be used to obtain noninteraction since the resulting compensated system would be unstable. It is shown that it is not possible to change these right-half plane zeros by either the well-known transfer-function design methods or by the state-variable feedback method. A combination of both transfer-function and state-variable techniques is discussed and shown to lower the order of the compensators required for the compensation of certain systems.