Optimal control of multirate sampled-data feedback systems via a polynomial approach

The linear quadratic Gaussian design of multirate-sampled multivariable feedback systems using input-output models is described. The theoretical emphasis is placed upon the formulation of augmented representations in which each variable is specified at its associated sample instants throughout one cycle of the sequence of sampling operations. The structures of the polynomial matrices utilised illuminate the causality issues involved and facilitate the acquisition of the optimal control solution from coupled diophantine equations.