Realisations of matrix transfer functions using RC ladders and summers

The design of a multivariable (multi-input/multi-output) control system or a multiport network often results in a multivariable compensator or a multiport filter which is described by a transfer-function matrix or a matrix transfer function. A state-space approach is presented to synthesise the matrix transfer function, using RC ladders and summers but not using integrators and multiwinding transformers. The Cauer I type RC ladder network is utilised to construct accessible states at which the feedback and feedforward gains can be practically implemented. A new similarity transformation matrix is derived to transform a state-space equation in a block companion form to a state-space equation in a block tridiagonal form.