Parameter dependence and controllability of convex processes with delay (Q700732)

The authors study the preservation of controllability for a delay differential inclusion of the form \[ \dot x(t)\in F(x(t),x(t-\Delta)), \quad \text{for a.e. } t\in [0,T] \] \[ x(t)=0, \quad \forall t\in [-\Delta,0[, \qquad x(0)\in K, \] where \(F: X\times X\to X,\) is a nonempty-valued closed convex process, \(X\) a finite-dimensional real Hilbert space, \(\Delta>0\) and \(K\) is a closed convex cone. The main theorem of this paper says that, under suitable assumptions (convexity, inner convergence and boundedness), the concept of controllability is stable with respect to a certain class of perturbations.