CONTROLLED AND CONDITIONED INVARIANT SUBSPACES IN LINEAR SYSTEM THEORY.
Technical rept. Jun-Jul 68,
CALIFORNIA UNIV BERKELEY DIV OF APPLIED MECHANICS
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The concept of invariance of a subspace under a linear transformation is strongly connected with controllability and observability problems of linear dynamical systems. In this paper we define controlled and conditioned 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 previously defined concepts concerning the determination of the constant output and perfect output controllability subspaces. Author