A New Stabilizing Control Law with Respect to a Control Lyapunov Function and Construction of Control Lyapunov Function for Particular Nonaffine Nonlinear Systems

In this paper, a new stabilizing control law with respect to a control Lyapunov function (CLF) is presented. This control law is similar to the pointwise min-norm control law. This control law is designed to maximize the angle between the gradient of the control Lyapunov function and the time derivative of the state vector at the state trajectory, which is defined in what follows as the 'pointwise maximum angle control law.' A comparison with the pointwise minnorm control law is provided. A criterion of the stability performance of control laws that are designed with respect to a CLF is presented. Also, by proposing the concept of the 'eigen-angle' for real square nonsingular matrices, the stabilization of some nonaffine nonlinear systems, and the construction of a CLF for such systems are reduced to the construction of CLFs for affine nonlinear (linear) systems. Finally, simulation results are provided to show the effectiveness of the proposed methodologies.