A new characterization of some structural properties of linear systems: unknown-input observability, invertibility and functional controllability†

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Abstract
A new approach for analysing some important structural properties of linear systems as unknown-input observability, invertibility and functional controllability, is presented. It is based on the concepts of ‘ controlled ’ and ‘ conditioned ’ invariance which have recently been developed and applied by the authors for a schematic and unitary treatment of many topics related to analysis and synthesis problems in linear system theory. The necessary and sufficient conditions herein derived are simple in their statement, can be quickly cheeked by means of a digital machine and have a geometrical meaning which tends to be very helpful for understanding their connection with other structural properties and for devising effective synthesis procedures.

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