Scientific publications

A problem of nonlinear systems stabilization is studied. Admissible controls are piecewise constant. The notion of normal local stabilizability is proposed. A point P(not necessary equilibrium) is normally locally stabilizable if for any τ>0 there exists such neighborhood D(P;< τ) of P that any point x∈D(P;< τ) can be steered, in a time less than τ, to any neighborhood of P and remains there. The constructive method of normal local stabilization of nonlinear autonomous systems is presented. This method involves a special sequence of contracting cylinders containing a trajectory. A domain of attraction of a given point is constructed.