ISSN:
1573-2878
Keywords:
Linear control systems
;
complete controllability
;
perturbations
;
convergence in measure
;
openness
;
density
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract LetL 1(I, ∝ n,n )×M(I, ℝ n,m ) be the space of all pairs (A, B), whereA andB are measurable functions from a compact intervalI to ℝ n,n and ℝ n,m , respectively, andA is Lebesgue integrable. Also, let this space be endowed with the topology of theL 1-norm with respect toA and the topology of convergence in measure with respect toB. Then, the set of all pairs (A, B), for which the corresponding linear control system $$(S)\dot x = A(t)x + B(t)u(t),a.e.t \in I,$$ is completely controllable onI, is shown to be open inL 1(I, ℝ n,n )×M(I, ℝ n,m ). It is also proved that, given any (A, B)∈L 1(I, ℝ n,n )×M(I, ℝ n,m ), (S) can be made completely controllable by means of an arbitrarily small perturbation ofB in the L∞-norm. These results are extensions of the analogous ones given by Dauer in the case when alsoB is integrable. Also, it is observed that a well-known complete control-lability criterion due to Conti works in the present case.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00941573
Permalink