Asymptotic bp-stabilization of a given closed invariant set of a smooth dynamical system (Q2420532)

The paper deals with the global asymptotic bp-stabilization of dynamical systems aiming at providing an explicit method to globally asymptotically \(bp\)-stabilize a closed invariant set determined by a smooth vector field. The essence of the result is that, given a smooth vector field \(X\in X(U)\) that generates a closed invariant set \(C\) of a dynamical system, for each \(\lambda>0\), a control vector field, \(X\lambda 0\) is constructed such that the perturbed dynamics produced by the vector field \(X+X\lambda 0\) is such that \(C\) attracts any bounded positive orbit of the perturbed system.