Global Stabilization of Nonlinear Dynamical Systems with Exponential Estimation of State Vector

A problem of equilibrium stabilization is considered for the nonlinear dynamical systems with feedback control using the system state estimation by the exponential observer - ad hoc dynamical system with exponential error decrease. Basic methods of creating exponential observers for nonlinear systems with control are given. The validity of the global dividing principle for a class of nonlinear systems is confirmed. A control law is obtained which stabilizes a specified position of the flexible single-link robot-manipulator using only measurements of angular position of the engine shaft.