Simultaneous stabilization of a class of multiplicatively perturbed plants

Necessary and sufficient conditions are obtained for stabilizability of a given linear, time-invariant, multi-input multi-output plant under unknown sensor failures of a prespecified channel. This problem is equivalent to simultaneous stabilization of a nominal plant and a multiplicatively perturbed plant, where the multiplicative perturbation is unknown but stable. A class of simultaneously stabilizing controllers are proposed for the nominal plant under such unknown perturbations.