Parameter-Dependent Control Lyapunov Functions for Stabilizing Nonlinear Parameter-Varying Systems

This paper introduces the concept of parameter-dependent (PD) control Lyapunov functions (CLFs) for gain-scheduled stabilization of nonlinear parameter-varying (NPV) systems. It shows that given a PD-CLF, a min-norm control law can be constructed by solving a robust quadratic program. For polynomial control-affine NPV systems, it provides convex conditions, based on the sum of squares programming, to jointly synthesize a PD-CLF and a PD controller, while maximizing the PD region of stabilization. Simulation results validate the efficacy of the proposed method.