Abstract
An algebraic description of (A,b)-invariant subspaces is presented, for the controllable and the uncontrollable case. These subspaces are generated by (A,b)-invariant vectors, classified in two kinds, and are used to determine the (A,b)-invariant subspaces in ker(C). These vectors are naturally associated with the roots of certain polynomials, and provide an alternate description of Morse’s transmission polynomials. Further the main result is presented, concerning an alternate description of the completeness, which is a central notion in the decentralized control of linear systems.
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