Constructive control Lyapunov functions for affine nonlinear systems with zero dynamics

The construction of control Lyapunov functions for affine nonlinear systems with zero dynamics is considered in this paper.A method is developed to ensure that a control Lyapunov function for the feedback linearizable part can be obtained by solving a Lyapunov equation.Using the control Lyapunov function of the feedback linearizable part and a Lyapunov function of the zero dynamics,a control Lyapunov function for the overall nonlinear system is then established by constructing a definite function.A state feedback is also designed to semiglobally stabilize the closed-loop system.Finally,a simulation example is given to illustrate the effectiveness of the design.