ISSN:
1573-2878
Keywords:
Infinite-dimensional systems
;
distributed control problem
;
stabilizability
;
controllability
;
semigroups
;
perturbations
;
feedback control
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract The questions of stabilizability of structurally perturbed or uncertain linear systems in Hilbert space of the form $$\dot x = (A + P(r))x + Bu$$ are considered. The operatorA is assumed to be the infinitesimal generator of aC 0-semigroup of contractionsT(t),t≥0, in a Hilbert spaceX;B is a bounded linear operator from another Hilbert spaceU toX; and {P(r),r ∈ Ω} is a family of bounded or unbounded perturbations ofA inX, where Ω is an arbitrary set, not necessarily carrying any topology. Sufficient conditions are presented that guarantee controllability and stabilizability of the perturbed system, given that the unperturbed system $$\dot x = Ax + Bu$$ has similar properties. In particular, it is shown that, for certain classes of perturbations, weak and strong stabilizability properties are preserved for the same state feedback operator.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00939936
Permalink
