Contributed Papers

Journal of Optimization Theory and Applications

, Volume 3, Issue 5, pp 306-315

First online:

Controlled and conditioned invariant subspaces in linear system theory

  • G. BasileAffiliated withInstitute of Electrotechnics, University of Bari
  • , G. MarroAffiliated withComputing and Servomechanism Center, University of Bologna

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


The concept of invariance of a subspace under a linear transformation is strongly connected with controllability and observability of linear dynamical systems. In this paper, we definecontrolled andconditioned invariant subspaces as a generalization of the simple invariants, for the purpose of investigating some further structural properties of linear systems. Moreover, we prove some fundamental theorems on which the computation of the above-mentioned subspaces is based. Then, we give two examples of practical application of the previous concepts concerning the determination of the constant output and perfect output controllability subspaces.