Global Control for a Class of Upper-Triangular Nonlinear Systems with Unknown Powers

This paper considers the global control problem for a class of uncertain upper-triangular nonlinear systems whose powers are not exactly known due to the model uncertainty. Under certain assumptions, a state-feedback controller, only involving the bounds of powers, is designed to make the nonlinear system locally stable by recursively constructing the Lyapunov functions with uncertain parameters. Then, based on the nested saturation method, it can be proved that the saturated control law is able to globally asymptotically stabilize the upper-triangular nonlinear systems with appropriate saturation level. Finally, a simulation example is presented to demonstrate the effectiveness of the proposed control scheme.