Statistical bounds on multivariable frequency response: an extension of the generalised Nyquist criterion

Statistical bounds for model parameters and corresponding system frequency-response limits are established. The results are extended to multivariable systems to produce an element-by-element characterisation of system uncertainty. This uncertainty representation can be used to develop frequency-response bounds on the eigenfunctions of perturbed multivariable systems; thus producing system gain and phase information via a generalised Nyquist analysis. An application of the technique is presented using a two-input/two-output system.