LMI based robust LSVF stabilization of a class of nonlinear systems

A method is proposed to design Linear Matrix Inequalities (LMI) based robust controllers for a class of nonlinear systems. Nonlinear functions are approximated by their upper bounds using convex-concave extensions. The contribution of the paper lies in the fact that the control law obtained is in the form of Linear State Variable Feedback (LSVF) and it is robust with respect to the parametric uncertainties. A new control Lyapunov function using Lie Derivatives is also introduced. A numerical example illustrates the steps of the design.