Given an observable system (C,A) € Km×n×Kn×n with K = R or C , the set of (C,A)- invariant subspaces having the restricted system fixed observability indices is a smooth manifold embedded on the corresponding Grassmannian. ...

Given a pair of matrices (A,B) we study the Lipschitz stability of its controlled invariant subspaces. A sufficient condition is derived from the geometry of the set formed by the quadruples (A,B, F, S) where S is ...

A natural equivalence relation can be considered in the generalized flag manifold. First we give a complete set of invariants of it as well as a canonical matrix description of the classes. Next we consider parametric ...

The geometry of the set of generalized partial realizations of a finite nice sequence of matrices is studied. It is proved that this set is a stratified manifold, the dimension of their strata is computed and its connection ...

Given a controllable linear control system defined by a pair of constant matrices (A,B), the set of controllability subspaces is a stratified submanifold of the set of (A,B)-invariant subspaces. We parametrize each strata ...

Given a bimodal system de¯ned by the equations ½ x_ (t) = A1x(t) + Bu(t) if ctx(t) · 0 x_ (t) = A2x(t) + Bu(t) if ctx(t) ¸ 0 (1) where B 2Mn;m and Ai 2Mn, i = 1; 2, are such that A1;A2 coincide on the hyper- plane V ...

Given a linear time invariant system with a disturbance we describe a method of finding the maximal dimensional output for a generic Disturbance Decoupling problem.