Commutative controller: a new technique for the design of multivariable control systems

If a linear time-invariant multiple-input multiple-output plant is represented by a square transfer-function matrix G(s), a spectral analysis may be carried out to determine a set of system characteristic transfer functions. A multivariable feedback controller may then be synthetised by first designing a set of single-loop controllers for these characteristic systems, and then transforming the results to obtain the required multivariable controller.