Reorientation of linear switched systems using state feedback

A characterisation is obtained for the controlled and conditioned invariants of a linear switched system under feedback. The existence of a maximal consistent subspace with feedback is shown and is computed. A few sufficient conditions under which the feedback has no effect on the controlled and conditioned invariants are obtained. Sufficient conditions for achieving the minimal jump subspace with feedback when it exists, were also derived. The impossibility of forcing the jump subspace to a trivial subspace with state feedback is shown. Some sufficient conditions on the feedback for the consistent and jump subspaces to intersect trivially have also been stated.