A Quadratic Lyapunov Function-Based Control Scheme for a Class of High-Order Nonlinear Systems

A very simple controller with completely new manner is designed for high-order nonlinear systems based on the quadratic Lyapunov functions (QLF) without adding a power integrator, which we mean the introduced Lyapunov function consists of the state errors commonly seen in the “one-order nonlinear systems” (defined at the beginning of Section II). Furthermore, a control scheme is present for the high-order nonlinear systems under two conditions. The main features of this note are that, this scheme provides a simple, new and effective way for high-order nonlinear system control, such that it is easily to be combined with the well-developed techniques used in one-order system control area benefiting from the QLF-based design frame. Simulation results illustrated the effectiveness of the provided scheme.